Modulated Bi-Orthogonal Polynomials on the Unit Circle: The $$2j-k$$ and $$j-2k$$ Systems
Modulated Bi-Orthogonal Polynomials on the Unit Circle: The $$2j-k$$ and $$j-2k$$ Systems
Abstract We construct the systems of bi-orthogonal polynomials on the unit circle where the Toeplitz structure of the moment determinants is replaced by $$\det (w_{2j-k})_{0\le j,k \le N-1} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>det</mml:mo> <mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>w</mml:mi> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>j</mml:mi> <mml:mo>-</mml:mo> <mml:mi>k</mml:mi> </mml:mrow> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> <mml:mo>≤</mml:mo> …