scholarly journals Elliptic Hypergeometric Laurent Biorthogonal Polynomials with a Dense Point Spectrum on the Unit Circle

2009 ◽  
Author(s):  
Satoshi Tsujimoto
Keyword(s):  
Unit Circle ◽  
Point Spectrum ◽  
Dense Point ◽  
Biorthogonal Polynomials

scholarly journals An Explicit Example of Polynomials Orthogonal on the Unit Circle with a Dense Point Spectrum Generated by a Geometric Distribution

2020 ◽  
Author(s):  
Alexei Zhedanov ◽  
Keyword(s):  
Unit Circle ◽  
Hypergeometric Function ◽  
Point Spectrum ◽  
Geometric Distribution ◽  
Dense Point

We present a new explicit family of polynomials orthogonal on the unit circle with a dense point spectrum. This family is expressed in terms of q-hypergeometric function of type 2phi1. The orthogonality measure is the wrapped geometric distribution. Some classical properties of the above polynomials are presented.

scholarly journals An algebraic treatment of the Askey biorthogonal polynomials on the unit circle

2021 ◽  
Vol 9 ◽  
Author(s):  
Luc Vinet ◽  
Alexei Zhedanov
Keyword(s):  
Unit Circle ◽  
Jacobi Polynomials ◽  
Algebraic Interpretation ◽  
Algebraic Treatment ◽  
Biorthogonal Polynomials

Abstract A joint algebraic interpretation of the biorthogonal Askey polynomials on the unit circle and of the orthogonal Jacobi polynomials is offered. It ties their bispectral properties to an algebra called the meta-Jacobi algebra $m\mathfrak {J}$ .

scholarly journals On a class of biorthogonal polynomials on the unit circle

2016 ◽  
Vol 438 (1) ◽  
pp. 465-473 ◽  
Author(s):  
J. Borrego-Morell ◽  
Fernando Rodrigo Rafaeli
Keyword(s):  
Unit Circle ◽  
Biorthogonal Polynomials

scholarly journals Some results on biorthogonal polynomials

1994 ◽  
Vol 17 (4) ◽  
pp. 625-636 ◽  
Author(s):  
Richard W. Ruedemann
Keyword(s):  
Analytic Continuation ◽  
Unit Circle ◽  
Lebesgue Measure ◽  
Laurent Polynomials ◽  
Biorthogonal Polynomials

Some biorthogonal polynomials of Hahn and Pastro are derived using a polynomial modification of the Lebesgue measuredθcombined with analytic continuation. A result is given for changing the measures of biorthogonal polynomials on the unit circle by the multiplication of their measures by certain Laurent polynomials.

On the Embedded Eigenvalues and Dense Point Spectrum of the Stark-Like Hamiltonians

1997 ◽  
Vol 183 (1) ◽  
pp. 185-200 ◽  
Author(s):  
Sergei N. Naboko ◽  
Alexander B. Pushnitski
Keyword(s):  
Point Spectrum ◽  
Dense Point ◽  
Embedded Eigenvalues
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