Certain problems of the approximation of functions in two variables by Fourier-Hermite sums in the space L sub(2)( Gamma [sup2 ], e super(-x) super([sup2 ]) super(-y) super([sup2 ]))

Certain problems of the approximation of functions in two variables by Fourier-Hermite sums in the space L sub(2)( Gamma [sup2 ], e super(-x) super([sup2 ]) super(-y) super([sup2 ]))

We give an exact estimate of the deviation of the "triangular" partial sums of the double Fourier-Hermite series of functions of the class L super(r) sub(2)(D) in the space L sub(2)( Gamma [sup2 ], e super(-x) super([sup2 ]) super(-y) super([sup2 ])).

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Veröffentlicht in:Analysis mathematica (Budapest) 2006-09, Vol.32 (3), p.163-171
Hauptverfasser: Abilov, V A, Abilov, M V
Format: Artikel
Sprache:eng
Schlagworte:
Approximation
Deviation
Estimates
Mathematical analysis
Mathematical models
Sums
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Zusammenfassung:We give an exact estimate of the deviation of the "triangular" partial sums of the double Fourier-Hermite series of functions of the class L super(r) sub(2)(D) in the space L sub(2)( Gamma [sup2 ], e super(-x) super([sup2 ]) super(-y) super([sup2 ])).
ISSN:0133-3852
1588-273X
DOI:10.1007/s10476-006-0009-6