@article{MTMT:33755338, title = {Almost Everywhere Convergence Questions of Series of Translates of Non-Negative Functions}, url = {https://m2.mtmt.hu/api/publication/33755338}, author = {Buczolich, Zoltán}, doi = {10.14321/realanalexch.48.1.1663223339}, journal-iso = {REAL ANALYSIS EXCHANGE}, journal = {REAL ANALYSIS EXCHANGE}, volume = {48}, unique-id = {33755338}, issn = {0147-1937}, year = {2023}, pages = {49-76}, orcid-numbers = {Buczolich, Zoltán/0000-0001-5481-8797} } @article{MTMT:32379535, title = {On the pair correlations of powers of real numbers}, url = {https://m2.mtmt.hu/api/publication/32379535}, author = {Aistleitner, Christoph and Baker, Simon}, doi = {10.1007/s11856-021-2130-4}, journal-iso = {ISR J MATH}, journal = {ISRAEL JOURNAL OF MATHEMATICS}, volume = {242}, unique-id = {32379535}, issn = {0021-2172}, abstract = {A classical theorem of Koksma states that for Lebesgue almost every x > 1 the sequence (x(n))n=1(infinity) is uniformly distributed modulo one. In the present paper we extend Koksma's theorem to the pair correlation setting. More precisely, we show that for Lebesgue almost every x > 1 the pair correlations of the fractional parts of (x(n))n=1(infinity) are asymptotically Poissonian. The proof is based on a martingale approximation method.}, year = {2021}, eissn = {1565-8511}, pages = {243-268} } @article{MTMT:32380655, title = {Effective Erdos-Wintner theorems for digital expansions}, url = {https://m2.mtmt.hu/api/publication/32380655}, author = {Drmota, Michael and Verwee, Johann}, doi = {10.1016/j.jnt.2021.04.006}, journal-iso = {J NUMBER THEORY}, journal = {JOURNAL OF NUMBER THEORY}, volume = {229}, unique-id = {32380655}, issn = {0022-314X}, abstract = {In 1972 Delange [9] observed in analogy of the classical Erdos-Wintner theorem that q -additive functions f (n) has a distribution function if and only if the two series Sigma f(dqj), Sigma f (dq(j))(2) converge. The purpose of this paper is to provide quantitative versions of this theorem as well as generalizations to other kinds of digital expansions. In addition to the qary and Cantor case we focus on the Zeckendorf expansion that is based on the Fibonacci sequence, where we provide a sufficient and necessary condition for the existence of a distribution function, namely that the two series Sigma f(F-j), Sigma f(F-j)(2) converge (previously only a sufficient condition was known [2]). (C) 2021 Elsevier Inc. All rights reserved.}, keywords = {Erdos-Wintner theorem; Digital expansions}, year = {2021}, eissn = {1096-1658}, pages = {218-260} } @article{MTMT:30767541, title = {Type 1 and 2 sets for series of translates of functions}, url = {https://m2.mtmt.hu/api/publication/30767541}, author = {Buczolich, Zoltán and Hanson, B. and Maga, Balázs and Vértesy, Gáspár}, doi = {10.1007/s10474-019-00937-2}, journal-iso = {ACTA MATH HUNG}, journal = {ACTA MATHEMATICA HUNGARICA}, volume = {158}, unique-id = {30767541}, issn = {0236-5294}, abstract = {Suppose Lambda is a discrete infinite set of nonnegative real numbers. We say that Lambda is type 1 if the series s(x)=Sigma lambda is an element of Lambda f(x+lambda) satisfies a zero-one law. This means that for any non-negative measurable f:R ->[0,+infinity) either the convergence set C(f,Lambda)={x:s(x)<+infinity}=R modulo sets of Lebesgue zero, or its complement the divergence set D(f,Lambda)={x:s(x)=+infinity}=R modulo sets of measure zero. If Lambda is not type 1 we say that Lambda is type 2.The exact characterization of type 1 and type 2 sets is not known. In this paper we continue our study of the properties of type 1 and 2 sets. We discuss sub and supersets of type 1 and 2 sets and give a complete and simple characterization of a subclass of dyadic type 1 sets. We discuss the existence of type 1 sets containing infinitely many elements independent over the rationals. Finally, we consider unions and Minkowski sums of type 1 and 2 sets.}, keywords = {Almost everywhere convergence; Borel-Cantelli lemma; Secondary 40A05; independence over the rationals; primary 28A20}, year = {2019}, eissn = {1588-2632}, pages = {271-293}, orcid-numbers = {Buczolich, Zoltán/0000-0001-5481-8797} } @article{MTMT:30812628, title = {Diffusive behavior of ergodic sums over rotations}, url = {https://m2.mtmt.hu/api/publication/30812628}, author = {Conze, J.-P. and Isola, S. and Le, Borgne S.}, doi = {10.1142/S0219493719500163}, journal-iso = {STOCH DYNAM}, journal = {STOCHASTICS AND DYNAMICS}, volume = {19}, unique-id = {30812628}, issn = {0219-4937}, abstract = {For a rotation by an irrational α on the circle and a BV function φ, we study the variance of the ergodic sums S Lφ (x):=σ j=0 L-1 φ(x + jα). When α is not of constant type, we construct sequences (LN) such that, at some scale, the ergodic sums SLNφ satisfy an ASIP. Explicit non-degenerate examples are given with an application to the rectangular periodic billiard in the plane. © 2019 World Scientific Publishing Company.}, keywords = {ROTATION; VARIANCE; central limit theorem; Subsequences; Lacunary series; Almost sure invariance principle; periodic rectangular billiard}, year = {2019}, eissn = {1793-6799} } @article{MTMT:3410311, title = {Random constructions for translates of non-negative functions}, url = {https://m2.mtmt.hu/api/publication/3410311}, author = {Buczolich, Zoltán and Hanson, B and Maga, Balázs and Vértesy, Gáspár}, doi = {10.1016/j.jmaa.2018.08.030}, journal-iso = {J MATH ANAL APPL}, journal = {JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS}, volume = {468}, unique-id = {3410311}, issn = {0022-247X}, abstract = {Suppose A is a discrete infinite set of nonnegative real numbers. We say that A is type 2 if the series s(x) = Sigma lambda Lambda f (x + lambda) does not satisfy a zero-one law. This means that we can find a non-negative measurable "witness function" f : R -> [0,+ infinity) such that both the convergence set C(f, Lambda) ={x : s(x) < + infinity} and its complement the divergence set D (f, Lambda) = {x : s(x) = +infinity} are of positive Lebesgue measure. If Lambda is not type 2 we say that A is type 1. The main result of our paper answers a question raised by Z. Buczolich, J-P. Kahane, and D. Mauldin. By a random construction we show that one can always choose a witness function which is the characteristic function of a measurable set. We also consider the effect on the type of a set A if we randomly delete its elements. Motivated by results concerning weighted sums Sigma c(n)f(nx)and the Khinchin conjecture, we also discuss some results about weighted sums}, keywords = {Almost everywhere convergence; Borel-Cantelli lemma; asymptotically dense; zero-one laws; Laws of large numbers}, year = {2018}, eissn = {1096-0813}, pages = {491-505}, orcid-numbers = {Buczolich, Zoltán/0000-0001-5481-8797} } @article{MTMT:2994059, title = {Convergence of series of dilated functions and spectral norms of GCD matrices}, url = {https://m2.mtmt.hu/api/publication/2994059}, author = {Aistleitner, C and Berkes, István and Seip, K and Weber, M}, doi = {10.4064/aa168-3-2}, journal-iso = {ACTA ARITH}, journal = {ACTA ARITHMETICA}, volume = {168}, unique-id = {2994059}, issn = {0065-1036}, keywords = {Probabilistic methods; Almost everywhere convergence; Sums of dilated functions; GCD sums; GCD matrices; Convergence of function series}, year = {2015}, eissn = {1730-6264}, pages = {221-246} } @article{MTMT:2994061, title = {GCD sums from Poisson integrals and systems of dilated functions}, url = {https://m2.mtmt.hu/api/publication/2994061}, author = {Aistleitner, C and Berkes, István and Seip, K}, doi = {10.4171/JEMS/537}, journal-iso = {J EUR MATH SOC}, journal = {JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY}, volume = {17}, unique-id = {2994061}, issn = {1435-9855}, abstract = {Upper bounds for GCD sums of the form (Formula Presented) are established, where (nk)1≤k≤N is any sequence of distinct positive integers and 0 < α ≤ 1; the estimate for α = 1/2 solves in particular a problem of Dyer and Harman from 1986, and the estimates are optimal except possibly for α = 1/2. The method of proof is based on identifying the sum as a certain Poisson integral on a polydisc; as a byproduct, estimates for the largest eigenvalues of the associated GCD matrices are also found. The bounds for such GCD sums are used to establish a Carleson - Hunt-type inequality for systems of dilated functions of bounded variation or belonging to Lip1/2, a result that in turn settles two longstanding problems on the a.e. behavior of systems of dilated functions: the a.e. growth of sums of the form (Formula Presented)=1 f(nkx) and the a.e. convergence of (Formula Presented)=1 ckf(nkx) when f is 1-periodic and of bounded variation or in Lip1/2. © European Mathematical Society 2015.}, keywords = {Spectral norm; Polydisc; Poisson integral; GCD sums and matrices; Convergence of series of dilated functions; Carleson-Hunt inequality}, year = {2015}, eissn = {1435-9863}, pages = {1517-1546} } @article{MTMT:25370501, title = {On some questions of VI Arnold on the stochasticity of geometric and arithmetic progressions}, url = {https://m2.mtmt.hu/api/publication/25370501}, author = {Aistleitner, Christoph}, doi = {10.1088/0951-7715/28/10/3663}, journal-iso = {NONLINEARITY}, journal = {NONLINEARITY}, volume = {28}, unique-id = {25370501}, issn = {0951-7715}, year = {2015}, eissn = {1361-6544}, pages = {3663-3675} } @article{MTMT:25263394, title = {The central limit theorem for complex Riesz-Raikov sums}, url = {https://m2.mtmt.hu/api/publication/25263394}, author = {Fukuyama, K and Kuri, N}, doi = {10.1016/j.crma.2015.04.020}, journal-iso = {CR MATH}, journal = {COMPTES RENDUS MATHEMATIQUE}, volume = {353}, unique-id = {25263394}, issn = {1631-073X}, year = {2015}, eissn = {1778-3569}, pages = {749-753} } @article{MTMT:26119245, title = {Quantitative uniform distribution results for geometric progressions}, url = {https://m2.mtmt.hu/api/publication/26119245}, author = {Aistleitner, C}, doi = {10.1007/s11856-014-1080-5}, journal-iso = {ISR J MATH}, journal = {ISRAEL JOURNAL OF MATHEMATICS}, volume = {204}, unique-id = {26119245}, issn = {0021-2172}, year = {2014}, eissn = {1565-8511}, pages = {155-197} } @article{MTMT:22947107, title = {Central limit theorem for stationary products of toral automorphisms}, url = {https://m2.mtmt.hu/api/publication/22947107}, author = {Conze, J-P and Le Borgne, S and Roger, M}, doi = {10.3934/dcds.2012.32.1597}, journal-iso = {DISCRETE CONT DYN S}, journal = {DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS SERIES A}, volume = {32}, unique-id = {22947107}, issn = {1078-0947}, year = {2012}, eissn = {1553-5231}, pages = {1597-1626} } @article{MTMT:22945716, title = {METRIC DISCREPANCY RESULTS FOR ERDOS-FORTET SEQUENCE}, url = {https://m2.mtmt.hu/api/publication/22945716}, author = {Fukuyama, K and Miyamoto, S}, doi = {10.1556/SScMath.2011.1186}, journal-iso = {STUD SCI MATH HUNG}, journal = {STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA}, volume = {49}, unique-id = {22945716}, issn = {0081-6906}, year = {2012}, eissn = {1588-2896}, pages = {52-78} } @article{MTMT:22945715, title = {Metric discrepancy results for subsequences of {theta (k) x}}, url = {https://m2.mtmt.hu/api/publication/22945715}, author = {Fukuyama, K and Hiroshima, N}, doi = {10.1007/s00605-010-0235-7}, journal-iso = {MONATSH MATH}, journal = {MONATSHEFTE FUR MATHEMATIK}, volume = {165}, unique-id = {22945715}, issn = {0026-9255}, year = {2012}, eissn = {1436-5081}, pages = {199-215} } @article{MTMT:22947111, title = {Limit law for some modified ergodic sums}, url = {https://m2.mtmt.hu/api/publication/22947111}, author = {Conze, J-P and Le Borgne, S}, doi = {10.1142/S021949371100319X}, journal-iso = {STOCH DYNAM}, journal = {STOCHASTICS AND DYNAMICS}, volume = {11}, unique-id = {22947111}, issn = {0219-4937}, year = {2011}, eissn = {1793-6799}, pages = {107-133} } @article{MTMT:2142559, title = {On the central limit theorem for f (nkx)}, url = {https://m2.mtmt.hu/api/publication/2142559}, author = {Aistleitner, C and Berkes, István}, doi = {10.1007/s00440-008-0190-6}, journal-iso = {PROBAB THEORY REL}, journal = {PROBABILITY THEORY AND RELATED FIELDS}, volume = {146}, unique-id = {2142559}, issn = {0178-8051}, abstract = {By a classical observation in analysis, lacunary subsequences of the trigonometric system behave like independent random variables: they satisfy the central limit theorem, the law of the iterated logarithm and several related probability limit theorems. For subsequences of the system (f(nx))n≥1 with 2π-periodic fεL2 this phenomenon is generally not valid and the asymptotic behavior of (f(nkx))k≥1 is determined by a complicated interplay between the analytic properties of f (e.g., the behavior of its Fourier coefficients) and the number theoretic properties of nk. By the classical theory, the central limit theorem holds for f (nkx) if nk = 2k, or if nk+1/nk → α with a transcendental α, but it fails e.g., for nk = 2k - 1. The purpose of our paper is to give a necessary and sufficient condition for f (nkx) to satisfy the central limit theorem. We will also study the critical CLT behavior of f (nkx), i.e., the question what happens when the arithmetic condition of the central limit theorem is weakened "infinitesimally". © Springer-Verlag 2008.}, keywords = {SEQUENCES; ASYMPTOTIC-BEHAVIOR; central limit theorem; TRIGONOMETRIC SERIES; Diophantine equations; Lacunary series; SIGMA-F(NKX); RIESZ-RAIKOV SUMS; NUMBER-THEORY}, year = {2010}, eissn = {1432-2064}, pages = {267-289} } @article{MTMT:26119254, title = {ON THE LAW OF THE ITERATED LOGARITHM FOR THE DISCREPANCY OF LACUNARY SEQUENCES}, url = {https://m2.mtmt.hu/api/publication/26119254}, author = {Aistleitner, C}, doi = {10.1090/S0002-9947-2010-05026-3}, journal-iso = {T AM MATH SOC}, journal = {TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY}, volume = {362}, unique-id = {26119254}, issn = {0002-9947}, year = {2010}, eissn = {1088-6850}, pages = {5967-5982} } @article{MTMT:169526, title = {On the convergence of sum c_kf(n_kx)}, url = {https://m2.mtmt.hu/api/publication/169526}, author = {Berkes, István and Weber, M}, doi = {10.1090/memo/0943}, journal-iso = {MEM AM MATH SOC}, journal = {MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY}, volume = {201}, unique-id = {169526}, issn = {0065-9266}, keywords = {BEHAVIOR; SEQUENCES; SERIES; ENTROPY; SPACE; martingales; Random walks; SUMS; THEOREMS; Discrepancy; Almost everywhere convergence; Lacunary series; Quasi-orthogonality; mean convergence; Dirichlet series; MOD-1; UNIFORM-DISTRIBUTION; random trigonometric series; NUMBER-THEORY}, year = {2009}, eissn = {1947-6221}, pages = {1-72} } @article{MTMT:22945720, title = {The law of the iterated logarithm for the discrepancies of a permutation of {n (k) x}}, url = {https://m2.mtmt.hu/api/publication/22945720}, author = {Fukuyama, K}, doi = {10.1007/s10474-008-8067-9}, journal-iso = {ACTA MATH HUNG}, journal = {ACTA MATHEMATICA HUNGARICA}, volume = {123}, unique-id = {22945720}, issn = {0236-5294}, year = {2009}, eissn = {1588-2632}, pages = {121-125} } @{MTMT:22946843, title = {The von Neumann theorem and spectral regularization}, url = {https://m2.mtmt.hu/api/publication/22946843}, author = {Weber, M}, booktitle = {DYNAMICAL SYSTEMS AND PROCESSES}, unique-id = {22946843}, year = {2009}, pages = {3-+} } @article{MTMT:22945721, title = {The law of the iterated logarithm for discrepancies of {theta(n)x}}, url = {https://m2.mtmt.hu/api/publication/22945721}, author = {Fukuyama, K}, doi = {10.1007/s10474-007-6201-8}, journal-iso = {ACTA MATH HUNG}, journal = {ACTA MATHEMATICA HUNGARICA}, volume = {118}, unique-id = {22945721}, issn = {0236-5294}, year = {2008}, eissn = {1588-2632}, pages = {155-170} } @inproceedings{MTMT:22945768, title = {The central limit theorem for non-conventional averages}, url = {https://m2.mtmt.hu/api/publication/22945768}, author = {Fukuyama, K}, booktitle = {Limit theorems in probability and statistics II}, unique-id = {22945768}, year = {2002}, pages = {77-90} } @article{MTMT:22328124, title = {Le théorème limite central pour les suites de R. C. Baker}, url = {https://m2.mtmt.hu/api/publication/22328124}, author = {K, Fukuyama and B, Petit}, doi = {10.1017/S0143385701001237}, journal-iso = {ERGOD THEOR DYN SYST}, journal = {ERGODIC THEORY AND DYNAMICAL SYSTEMS}, volume = {21}, unique-id = {22328124}, issn = {0143-3857}, year = {2001}, eissn = {1469-4417}, pages = {479-492} } @article{MTMT:22945741, title = {The central limit theorem for ∑ f(θn x)g(θn2 x)}, url = {https://m2.mtmt.hu/api/publication/22945741}, author = {Fukuyama, K}, doi = {10.1017/S0143385700000729}, journal-iso = {ERGOD THEOR DYN SYST}, journal = {ERGODIC THEORY AND DYNAMICAL SYSTEMS}, volume = {20}, unique-id = {22945741}, issn = {0143-3857}, year = {2000}, eissn = {1469-4417}, pages = {1335-1353} } @article{MTMT:1738274, title = {A Probability Limit Theorem for {f(nx)}}, url = {https://m2.mtmt.hu/api/publication/1738274}, author = {Péter, Erika}, doi = {10.1023/A:1006716931963}, journal-iso = {ACTA MATH HUNG}, journal = {ACTA MATHEMATICA HUNGARICA}, volume = {87}, unique-id = {1738274}, issn = {0236-5294}, year = {2000}, eissn = {1588-2632}, pages = {23-31} } @article{MTMT:167577, title = {A limit theorem for lacunary series summa f(nkx)}, url = {https://m2.mtmt.hu/api/publication/167577}, author = {Berkes, István and Philipp, W}, journal-iso = {STUD SCI MATH HUNG}, journal = {STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA}, volume = {34}, unique-id = {167577}, issn = {0081-6906}, keywords = {Lacunary series; law of the iterated logarithm}, year = {1998}, eissn = {1588-2896}, pages = {1-13} } @article{MTMT:22945744, title = {Riesz-raikov sums and weyl transform}, url = {https://m2.mtmt.hu/api/publication/22945744}, author = {Fukuyama, K}, journal-iso = {MONTE CARLO METH APPL}, journal = {MONTE CARLO METHODS AND APPLICATIONS}, volume = {2}, unique-id = {22945744}, issn = {0929-9629}, year = {1996}, eissn = {1569-3961}, pages = {271-293} } @article{MTMT:22945769, title = {THE CENTRAL-LIMIT-THEOREM FOR RIESZ-RAIKOV SUMS}, url = {https://m2.mtmt.hu/api/publication/22945769}, author = {FUKUYAMA, K}, doi = {10.1007/BF01204953}, journal-iso = {PROBAB THEORY REL}, journal = {PROBABILITY THEORY AND RELATED FIELDS}, volume = {100}, unique-id = {22945769}, issn = {0178-8051}, year = {1994}, eissn = {1432-2064}, pages = {57-75} } @article{MTMT:22945770, title = {FUNCTIONAL LAW OF THE ITERATED LOGARITHM FOR LACUNARY TRIGONOMETRIC AND SOME GAP SERIES}, url = {https://m2.mtmt.hu/api/publication/22945770}, author = {FUKUYAMA, K}, journal-iso = {J MATH KYOTO U}, journal = {JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY}, volume = {32}, unique-id = {22945770}, issn = {0023-608X}, year = {1992}, pages = {967-987} } @article{MTMT:25748824, title = {VARIANTS ON THE LAW OF THE ITERATED LOGARITHM}, url = {https://m2.mtmt.hu/api/publication/25748824}, author = {BINGHAM, NH}, doi = {10.1112/blms/18.5.433}, journal-iso = {B LOND MATH SOC}, journal = {BULLETIN OF THE LONDON MATHEMATICAL SOCIETY}, volume = {18}, unique-id = {25748824}, issn = {0024-6093}, year = {1986}, eissn = {1469-2120}, pages = {432-467} } @article{MTMT:22945772, title = {ON THE APPROXIMATION OF LACUNARY SERIES BY BROWNIAN-MOTION}, url = {https://m2.mtmt.hu/api/publication/22945772}, author = {KAUFMAN, R}, doi = {10.1007/BF01896825}, journal-iso = {ACTA MATH ACAD SCI HUNG}, journal = {ACTA MATHEMATICA ACADEMIAE SCIENTIARUM HUNGARICAE}, volume = {35}, unique-id = {22945772}, issn = {0001-5954}, year = {1980}, pages = {61-66} } @article{MTMT:22945773, title = {COUNTEREXAMPLES IN ERGODIC THEORY AND NUMBER THEORY}, url = {https://m2.mtmt.hu/api/publication/22945773}, author = {DELJUNCO, A and ROSENBLATT, J}, doi = {10.1007/BF01673506}, journal-iso = {MATH ANN}, journal = {MATHEMATISCHE ANNALEN}, volume = {245}, unique-id = {22945773}, issn = {0025-5831}, year = {1979}, eissn = {1432-1807}, pages = {185-197} } @article{MTMT:1926655, title = {An a.s. invariance principle for lacunary series f(nkx)}, url = {https://m2.mtmt.hu/api/publication/1926655}, author = {Berkes, István and W, Philipp}, doi = {10.1007/BF01902603}, journal-iso = {ACTA MATH ACAD SCI HUNG}, journal = {ACTA MATHEMATICA ACADEMIAE SCIENTIARUM HUNGARICAE}, volume = {34}, unique-id = {1926655}, issn = {0001-5954}, year = {1979}, pages = {141-155} } @article{MTMT:1926682, title = {On a central limit theorem for lacunary trigonometric series}, url = {https://m2.mtmt.hu/api/publication/1926682}, author = {Berkes, István}, doi = {10.1007/BF01908987}, journal-iso = {ANAL MATH}, journal = {ANALYSIS MATHEMATICA}, volume = {4}, unique-id = {1926682}, issn = {0133-3852}, year = {1978}, eissn = {1588-273X}, pages = {159-180} } @article{MTMT:22945775, title = {FUNCTIONAL LAW OF ITERATED LOGARITHM FOR EMPIRICAL DISTRIBUTION FUNCTIONS OF WEAKLY DEPENDENT RANDOM-VARIABLES}, url = {https://m2.mtmt.hu/api/publication/22945775}, author = {PHILIPP, W}, journal-iso = {ANN PROBAB}, journal = {ANNALS OF PROBABILITY}, volume = {5}, unique-id = {22945775}, issn = {0091-1798}, year = {1977}, eissn = {2168-894X}, pages = {349-350} } @article{MTMT:2142576, title = {On the asymptotic behaviour of {perspective}f(nkx) - Applications}, url = {https://m2.mtmt.hu/api/publication/2142576}, author = {Berkes, István}, doi = {10.1007/BF00535968}, journal-iso = {Z WAHRSC VERW GEBIETE}, journal = {ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE}, volume = {34}, unique-id = {2142576}, issn = {0044-3719}, year = {1976}, pages = {347-365} }