A Sequence Algebra of Finite Sections, Convolution, and Multiplication Operators on LP()

作者：Roch Steffen; Santos Pedro A^*; Silbermann Bernd

来源：Numerical Functional Analysis and Optimization, 2010, 31(1): 45-77.

DOI：10.1080/01630560903574977

• Convolution operators
• Finite sections method
• Operator algebras
• Stability
• Wiener-Hopf operators

This paper is concerned with the applicability of the finite sections method to operators belonging to the closed subalgebra of L(Lp()), 1p , generated by operators of multiplication by piecewise continuous functions in [image omitted] and operators of convolution by piecewise continuous Fourier multipliers. For this, we introduce a larger algebra of sequences, which contains the sequences that interest us and the usual operator algebra generated by the operators of multiplication and convolution. There is a direct relationship between the applicability of the finite sections method for a given operator and invertibility of the corresponding sequence in this algebra. Exploring this relationship and using local principles, we construct locally equivalent representations that allow one to derive invertibility criteria.

• 出版日期2010