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On Mean Convergence of Fourier‐Bessel Series of Negative Order
Author(s) -
Benedek A.,
Panzone R.
Publication year - 1971
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1971503281
Subject(s) - bessel function , mathematics , fourier series , series (stratigraphy) , order (exchange) , mathematical analysis , fourier transform , convergence (economics) , space (punctuation) , integrable system , pure mathematics , paleontology , linguistics , philosophy , finance , economics , biology , economic growth
The expansion of f ∈ L p (0, 1) Fourier series of Bessel functions of order converges to f in L p wheneverLet be the space of p ‐integrable functions with respect to the measure t dt and where { s n }, n = 1, 2, …, is the set of positive zeros of J v . Then, the expansion of in a Fourier series of functions ψ n , −1 < ν < −½, converges to in whenever