Convergence almost Everywhere of Certain Partial Sums of Fourier Integrals | Zendy

Carbery Anthony | Zendy; Gorges Dirk | Zendy; Marletta Gianfranco | Zendy; Thiele Christoph | Zendy

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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.

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