TY - JOUR AU - Buczolich, Zoltán AU - Maga, Balázs AU - Vértesy, Gáspár TI - On Series of Translates of Positive Functions. III JF - ANALYSIS MATHEMATICA J2 - ANAL MATH VL - 44 PY - 2018 IS - 2 SP - 185 EP - 205 PG - 21 SN - 0133-3852 DO - 10.1007/s10476-018-0205-1 UR - https://m2.mtmt.hu/api/publication/3390326 ID - 3390326 N1 - Cited By :2 Export Date: 9 September 2022 CODEN: ANMAD Correspondence Address: Buczolich, Z.; Department of Analysis, Pázmány Péter sétány 1/c, Hungary; email: buczo@cs.elte.hu LA - English DB - MTMT ER - TY - JOUR AU - Aistleitner, C AU - Berkes, István AU - Seip, K AU - Weber, M TI - Convergence of series of dilated functions and spectral norms of GCD matrices JF - ACTA ARITHMETICA J2 - ACTA ARITH VL - 168 PY - 2015 IS - 3 SP - 221 EP - 246 PG - 26 SN - 0065-1036 DO - 10.4064/aa168-3-2 UR - https://m2.mtmt.hu/api/publication/2994059 ID - 2994059 LA - English DB - MTMT ER - TY - JOUR AU - Berkes, István AU - Weber, M TI - On series Σckf(kx) and Khinchin’s conjecture JF - ISRAEL JOURNAL OF MATHEMATICS J2 - ISR J MATH VL - 201 PY - 2014 IS - 2 SP - 593 EP - 609 PG - 17 SN - 0021-2172 DO - 10.1007/s11856-014-0036-0 UR - https://m2.mtmt.hu/api/publication/2780054 ID - 2780054 N1 - WoS:hiba:000343148600005 2019-03-03 01:01 cím nem egyezik AB - We prove the optimality of a criterion of Koksma (1953) in Khinchin’s conjecture on strong uniform distribution. This verifies a claim of Bourgain (1988) and leads also to a near optimal a.e. convergence condition for series Σk=1 ∞ckf(kx) with f ∈ L2. Finally, we show that under mild regularity conditions on the Fourier coefficients of f, the Khinchin conjecture is valid assuming only f ∈ L2. LA - English DB - MTMT ER - TY - JOUR AU - Berkes, István AU - Weber, M TI - On the convergence of sum c_kf(n_kx) JF - MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY J2 - MEM AM MATH SOC VL - 201 PY - 2009 IS - 943 SP - 1 EP - 72 PG - 72 SN - 0065-9266 DO - 10.1090/memo/0943 UR - https://m2.mtmt.hu/api/publication/169526 ID - 169526 LA - English DB - MTMT ER - TY - JOUR AU - Buczolich, Zoltán AU - Kahane, JP AU - Mauldin, RD TI - On series of translates of positive functions JF - ACTA MATHEMATICA HUNGARICA J2 - ACTA MATH HUNG VL - 93 PY - 2001 IS - 3 SP - 171 EP - 188 PG - 18 SN - 0236-5294 DO - 10.1023/A:1013904610368 UR - https://m2.mtmt.hu/api/publication/1390271 ID - 1390271 AB - For Lambda, a discrete infinite set of nonnegative real numbers, and a nonnegative measurable function f : R - R+, consider C = C(f, Lambda) = {x : SigmalambdaepsilonLambda f(x + Lambda) < +00 }. The sets Lambda naturally break into two types. Type 1 consists of Lambda such that either C = R almost everywhere or else C = 0 a.e., for every f. Type 2 consists of all the other A. We introduce a notion of asymptotic density for Lambda and the complementary notion of asymptotic lacunarity. We demonstrate that Lambda is of type 2 if it is asymptotically lacunary or else is asymptotically dense and exhibits asymptotically large Q-independent sets. We also give some examples of sets of both types. LA - English DB - MTMT ER - TY - JOUR AU - Buczolich, Zoltán AU - Kahane, JP AU - Mauldin, RD TI - On series of translates of positives functions JF - COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE J2 - CR ACAD SCI I MATH VL - 329 PY - 1999 IS - 4 SP - 261 EP - 264 PG - 4 SN - 0764-4442 DO - 10.1016/S0764-4442(00)88563-8 UR - https://m2.mtmt.hu/api/publication/1390280 ID - 1390280 AB - Given f : R --> R+ and Lambda discrete in R+ we denote by C(f, Lambda), resp. D(f, Lambda), the x-set where the series Sigma f(x + lambda) (lambda is an element of Lambda) converges, resp. diverges. The sets Lambda break into two types. Type 1 consists of Lambda such that the Lebesgue measure of either C(f, Lambda) or D(f, Lambda) vanishes whatever f measurable, and type 2 consists of all the other Lambda. Buczolich and Mauldin proved that {log n} (n = 1, 2,...) is of type 2. Type 2 is generic, type 1 is rare, and we give examples of both cases (Theorems 1, 2, 3). (C) 1999 Academie des Sciences / Editions scientifiques et medicales Elsevier SAS. LA - French DB - MTMT ER - TY - JOUR AU - Buczolich, Zoltán AU - Mauldin, RD TI - On the convergence of Sigma(infinity)(n=1)f(nx) for measurable functions JF - MATHEMATIKA J2 - MATHEMATIKA VL - 46 PY - 1999 IS - 2 SP - 337 EP - 341 PG - 5 SN - 0025-5793 DO - 10.1112/S0025579300007804 UR - https://m2.mtmt.hu/api/publication/2380646 ID - 2380646 N1 - Part number: 2 WoS:hiba:000169042300008 2020-08-29 10:29 cím nem egyezik AB - Questions of Haight and of Weizsäcker are answered in the following result. There exists a measurable function f: (0, +∞) → {0, 1} and two non-empty intervals IF, I∞ ⊂[1/2, 1) such that Σ∞ n = 1 f(nx) < +∞ for every x∈I∞, and Σ∞ n = 1 f(nx) <+∞ for almost every x∈IF. The function f may be taken to be the characteristic function of an open set E. LA - English DB - MTMT ER - TY - JOUR AU - Berkes, István TI - On the asymptotic behaviour of {perspective}f(nkx) - Applications JF - ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE J2 - Z WAHRSC VERW GEBIETE VL - 34 PY - 1976 IS - 4 SP - 347 EP - 365 PG - 19 SN - 0044-3719 DO - 10.1007/BF00535968 UR - https://m2.mtmt.hu/api/publication/2142576 ID - 2142576 N1 - WoS:hiba:A1976BM63700006 2019-03-02 22:35 cím nem egyezik LA - English DB - MTMT ER - TY - JOUR AU - Berkes, István TI - On the asymptotic behaviour of {perspective}f(nkx) - Main theorems JF - ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE J2 - Z WAHRSC VERW GEBIETE VL - 34 PY - 1976 IS - 4 SP - 319 EP - 345 PG - 27 SN - 0044-3719 DO - 10.1007/BF00535967 UR - https://m2.mtmt.hu/api/publication/2142577 ID - 2142577 N1 - WoS:hiba:A1976BM63700005 2019-03-02 22:35 cím nem egyezik LA - English DB - MTMT ER -