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Symbol and characteristic of weakly singular integral operators

Swanhild Bernstein

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Abstract

A basic notion of pseudodifferential operators or singular integral operators is the symbol. We want to give a formula for the symbol of weakly singular integral operators. This gives a simple connection between weakly singular integral operators and a special class of pseudodifferential operators. The case of singular integral operators is included. In this way we are able to use the theory of symbols also for weakly singular integral operators.

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What this paper is about

A basic notion of pseudodifferential operators or singular integral operators is the symbol. We want to give a formula for the symbol of weakly singular integral operators. This gives a simple connection between weakly singular integral operators and a special class of pseudodifferential operators. The case of singular integral operators is included. In this way we are able to use the theory of symbols also for weakly singular integral operators.

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Available abstract

A basic notion of pseudodifferential operators or singular integral operators is the symbol. We want to give a formula for the symbol of weakly singular integral operators. This gives a simple connection between weakly singular integral operators and a special class of pseudodifferential operators. The case of singular integral operators is included. In this way we are able to use the theory of symbols also for weakly singular integral operators.

Key concepts: Mathematics, Fourier integral operator, Singular integral, Singular integral operators, Singular integral operators of convolution type, Symbol (formal), Microlocal analysis, Operator theory

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