Some Spectral Geometry Inequalities for Generalized Heat Potential Operators

Aidyn Kassymov, Durvudkhan Suragan

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

In this paper we prove that the circular cylinder is a maximizer of the Schatten p-norm of generalized heat potential operators among all Euclidean cylindric domains of a given measure. We also show that the equilateral triangular cylinder has the largest Schatten p-norm among all triangular cylinders of a given measure. Cylindric analogues of the Rayleigh–Faber–Krahn inequalities are established in both cases as well. We also give an analogue of a Hong–Krahn–Szegö type inequality.

Original languageEnglish
Pages (from-to)1371-1385
Number of pages15
JournalComplex Analysis and Operator Theory
Volume11
Issue number6
DOIs
Publication statusPublished - Aug 1 2017
Externally publishedYes

Fingerprint

Spectral Geometry
Potential Operators
Circular cylinders
Mathematical operators
Triangular
Heat
Analogue
Equilateral
Norm
Geometry
Circular Cylinder
Euclidean
Hot Temperature

Keywords

  • Eigenvalue
  • Heat potential operator
  • Hong–Krahn–Szegö inequality
  • Rayleigh–Faber–Krahn inequality
  • Schatten p-norm

ASJC Scopus subject areas

  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

Cite this

Some Spectral Geometry Inequalities for Generalized Heat Potential Operators. / Kassymov, Aidyn; Suragan, Durvudkhan.

In: Complex Analysis and Operator Theory, Vol. 11, No. 6, 01.08.2017, p. 1371-1385.

Research output: Contribution to journalArticle

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