scholarly journals Orthogonal expansions related to compact Gelfand pairs

2018 ◽  
Vol 36 (3-4) ◽  
pp. 259-277 ◽  
Author(s):  
Christian Berg ◽  
Ana P. Peron ◽  
Emilio Porcu
Keyword(s):  
Gelfand Pairs ◽  
Orthogonal Expansions

Spherical functions for Gelfand pairs associated with compact groupoids

2015 ◽  
Vol 27 (3-4) ◽  
pp. 573-582
Author(s):  
Ibrahima Toure ◽  
Kinvi Kangni
Keyword(s):  
Spherical Functions ◽  
Gelfand Pairs

scholarly journals Trees, wreath products and finite Gelfand pairs

2006 ◽  
Vol 206 (2) ◽  
pp. 503-537 ◽  
Author(s):  
Tullio Ceccherini-Silberstein ◽  
Fabio Scarabotti ◽  
Filippo Tolli
Keyword(s):  
Wreath Products ◽  
Gelfand Pairs

scholarly journals Orthogonal structure on a quadratic curve

2020 ◽  
Author(s):  
Sheehan Olver ◽  
Yuan Xu
Keyword(s):  
Weight Function ◽  
Orthogonal Polynomials ◽  
Extension Problem ◽  
Orthogonal Expansions ◽  
Schrödinger’S Equation ◽  
Fourier Extension ◽  
Quadratic Curve ◽  
Interpolation Of Functions ◽  
Fourier Orthogonal Expansions ◽  
Schrödinger's Equation

Abstract Orthogonal polynomials on quadratic curves in the plane are studied. These include orthogonal polynomials on ellipses, parabolas, hyperbolas and two lines. For an integral with respect to an appropriate weight function defined on any quadratic curve, an explicit basis of orthogonal polynomials is constructed in terms of two families of orthogonal polynomials in one variable. Convergence of the Fourier orthogonal expansions is also studied in each case. We discuss applications to the Fourier extension problem, interpolation of functions with singularities or near singularities and the solution of Schrödinger’s equation with nondifferentiable or nearly nondifferentiable potentials.

scholarly journals Gelfand pairs on the Heisenberg group and Schwartz functions

2009 ◽  
Vol 256 (5) ◽  
pp. 1565-1587 ◽  
Author(s):  
Francesca Astengo ◽  
Bianca Di Blasio ◽  
Fulvio Ricci
Keyword(s):  
Heisenberg Group ◽  
Gelfand Pairs ◽  
Schwartz Functions
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