Finite Section Method for a Banach Algebra of Convolution Type Operators on L-p(R) with Symbols Generated by PC and SO

Oleksiy Karlovych

doi:10.1007/s00020-010-1784-9

Finite Section Method for a Banach Algebra of Convolution Type Operators on L-p(R) with Symbols Generated by PC and SO

Oleksiy Karlovych

DM - Departamento de Matemática

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

We prove necessary and sufficient conditions for the applicability of the finite section method to an arbitrary operator in the Banach algebra generated by the operators of multiplication by piecewise continuous functions and the convolution operators with symbols in the algebra generated by piecewise continuous and slowly oscillating Fourier multipliers on L-p(R), 1 < p < infinity.

Original language	Unknown
Pages (from-to)	559-600
Journal	Integral Equations And Operator Theory
Volume	67
Issue number	4
DOIs	https://doi.org/10.1007/s00020-010-1784-9
Publication status	Published - 1 Jan 2010

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10.1007/s00020-010-1784-9

Cite this

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title = "Finite Section Method for a Banach Algebra of Convolution Type Operators on L-p(R) with Symbols Generated by PC and SO",

abstract = "We prove necessary and sufficient conditions for the applicability of the finite section method to an arbitrary operator in the Banach algebra generated by the operators of multiplication by piecewise continuous functions and the convolution operators with symbols in the algebra generated by piecewise continuous and slowly oscillating Fourier multipliers on L-p(R), 1 < p < infinity.",

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N2 - We prove necessary and sufficient conditions for the applicability of the finite section method to an arbitrary operator in the Banach algebra generated by the operators of multiplication by piecewise continuous functions and the convolution operators with symbols in the algebra generated by piecewise continuous and slowly oscillating Fourier multipliers on L-p(R), 1 < p < infinity.

AB - We prove necessary and sufficient conditions for the applicability of the finite section method to an arbitrary operator in the Banach algebra generated by the operators of multiplication by piecewise continuous functions and the convolution operators with symbols in the algebra generated by piecewise continuous and slowly oscillating Fourier multipliers on L-p(R), 1 < p < infinity.

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KW - algebraization

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KW - local

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KW - homogenization

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