ON A CLASS OF POLYNOMIALS DEFINED BY TWO ORTHOGONALITY RELATIONS

1981 ◽  
Vol 38 (4) ◽  
pp. 563-580 ◽  
Author(s):  
V A Kaljagin
Keyword(s):  
Orthogonality Relations

scholarly journals Square-integrable representations of non-unimodular groups

1976 ◽  
Vol 15 (1) ◽  
pp. 1-12 ◽  
Author(s):  
A.L. Carey
Keyword(s):  
Hilbert Space ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Hilbert Algebra ◽  
Technical Tool ◽  
Integrable Representation ◽  
Hilbert Algebras ◽  
Orthogonality Relations ◽  
Square Integrable Representation ◽  
Main Technical Tool

In the last three years a number of people have investigated the orthogonality relations for square integrable representations of non-unimodular groups, extending the known results for the unimodular case. The results are stated in the language of left (or generalized) Hilbert algebras. This paper is devoted to proving the orthogonality relations without recourse to left Hilbert algebra techniques. Our main technical tool is to realise the square integrable representation in question in a reproducing kernel Hilbert space.

scholarly journals Orthogonality relations among modes in left-handed materials slab waveguide

2006 ◽  
Vol 55 (4) ◽  
pp. 1846
Author(s):  
Zhang Gao-Ming ◽  
Peng Jing-Cui ◽  
Jian Zhi-Jian ◽  
Huang Xiao-Yi
Keyword(s):  
Slab Waveguide ◽  
Left Handed ◽  
Orthogonality Relations

SLn, Orthogonality Relations and Transfer

2007 ◽  
Vol 59 (3) ◽  
pp. 449-464 ◽  
Author(s):  
Alexandru Ioan Badulescu
Keyword(s):  
Division Algebra ◽  
Local Field ◽  
Finite Dimension ◽  
Complex Conjugate ◽  
Orbital Integrals ◽  
Central Division ◽  
Zero Characteristic ◽  
Central Division Algebra ◽  
Orthogonality Relations ◽  
Square Integrable Representation

AbstractLet π be a square integrable representation of G′ = SLn(D), with D a central division algebra of finite dimension over a local field F of non-zero characteristic. We prove that, on the elliptic set, the character of π equals the complex conjugate of the orbital integral of one of the pseudocoefficients of π. We prove also the orthogonality relations for characters of square integrable representations of G′. We prove the stable transfer of orbital integrals between SLn(F) and its inner forms.

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