Fourier Series and Right Invertible Operators

✍ Scribed by Franz- Jürgen Delvos

• Publisher: John Wiley and Sons
• Year: 1985
• Tongue: English
• Weight: 297 KB
• Volume: 122
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19851220109

✦ Synopsis

In several papers [S, 9, 101 M. TASCHE has applied the algebraic theory of right invertible operators [ . ; I to problems of interpolat.ion and approximation. In a recent paper [2] we used the method of parametric extension to construct right invertible operators in spaces of bivariate continuous functions. right invertible operator in the linear space C(J2) of bivariate continuous functions on the square JZ (J=[O, %I) which is related to the expansion of bivariate functions into double FOURIER series. In particuIar, we will derive a decomposition formula for smooth functions in C'J(J2) which yields as D special application the absolute convergence of the double FOURIER series of (t periodic function in C'.'(J2).