Advances in Operator Theory
- Adv. Oper. Theory
- Volume 2, Number 2 (2017), 179-191.
On spectral synthesis in several variables
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.
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
Permanent link to this document
Digital Object Identifier
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
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