Advances in Operator Theory

On spectral synthesis in several variables

László Székelyhidi

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Gelfand pair spherical function spherical monomial spectral synthesis


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

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