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Convergence almost Everywhere of Certain Partial Sums of Fourier Integrals
Author(s) -
Carbery Anthony,
Gorges Dirk,
Marletta Gianfranco,
Thiele Christoph
Publication year - 2003
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609302001728
Subject(s) - mathematics , almost everywhere , lacunary function , infinity , fourier transform , convergence (economics) , order (exchange) , fourier series , mathematics subject classification , inverse , pure mathematics , mathematical analysis , geometry , economics , economic growth , finance
Suppose that R goes to infinity through a second‐order lacunary set. Let S R denote the R th spherical partial inverse Fourier integral on R d . Then S R f converges almost everywhere to f , provided that f satisfies∫∣ f ^ ( ξ ) log ( 8 + ∣ ξ ∣ ) ∣ 2 d ξ < ∞ .2000 Mathematics Subject Classification 42B15, 42B25, 42B08.