Advances in Operator Theory

On spectral synthesis in several variables

László Székelyhidi

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Abstract

In a recent paper we proposed a possible generalization of L. Schwartz's classical spectral synthesis result for continuous functions in several variables. The idea is based on Gelfand pairs and spherical functions while "translation invariance" is replaced by invariance with respect to the action of affine groups. In this paper we describe the function classes which play the role of the exponential monomials in this setting.

Article information

Source
Adv. Oper. Theory, Volume 2, Number 2 (2017), 179-191.

Dates
Received: 10 October 2017
Accepted: 8 March 2017
First available in Project Euclid: 4 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.aot/1512431564

Digital Object Identifier
doi:10.22034/aot.1610-1028

Mathematical Reviews number (MathSciNet)
MR3730067

Zentralblatt MATH identifier
1370.43002

Subjects
Primary: 43A45: Spectral synthesis on groups, semigroups, etc.
Secondary: 43A90: Spherical functions [See also 22E45, 22E46, 33C55] 47B38: Operators on function spaces (general) 22D15: Group algebras of locally compact groups

Keywords
Gelfand pair spherical function spherical monomial spectral synthesis

Citation

Székelyhidi, László. On spectral synthesis in several variables. Adv. Oper. Theory 2 (2017), no. 2, 179--191. doi:10.22034/aot.1610-1028. https://projecteuclid.org/euclid.aot/1512431564


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