Biorthogonal polynomials and zero-mapping transformations

Details Biorthogonal polynomials and zero-mapping transformations Biorthogonal polynomials and zero-mapping transformations

1994-04-22

arxiv.org/abs/math/9404223v1

Mathematics

Classical Analysis and ODEs

Scientific paper

The authors have presented in \cite{IN2} a technique to generate transformations $\cal T$ of the set ${\Bbb P}_n$ of $n$th degree polynomials to itself such that if $p\in{\Bbb P}_n$ has all its zeros in $(c,d)$ then ${\cal T}\{p\}$ has all its zeros in $(a,b)$, where $(a,b)$ and $(c,d)$ are given real intervals. The technique rests upon the derivation of an explicit form of biorthogonal polynomials whose Borel measure is strictly sign consistent and such that the ratio of consecutive generalized moments is a rational $[1/1]$ function of the parameter. Specific instances of strictly sign consistent measures that have been debated in \cite{IN2} include $x^\mu\D\psi(x)$, $\mu^x\D\psi(x)$ and $x^{\log_q\mu}\D\psi(x)$, $q\in(0,1)$. In this paper we identify all measures $\psi$ such that their consecutive generalized moments have a rational $[1/1]$ quotient, thereby characterizing all possible zero-mapping transformations of this kind.

Affiliated with

Also associated with

No associations

Rating

Biorthogonal polynomials and zero-mapping transformations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Biorthogonal polynomials and zero-mapping transformations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Biorthogonal polynomials and zero-mapping transformations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-708011