On the zeros of some continuous analogues of matrix orthogonal polynomials and a related extension problem with negative squares | Zendy

Dym Harry | Zendy

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On the zeros of some continuous analogues of matrix orthogonal polynomials and a related extension problem with negative squares

Author(s) -

Dym Harry

Publication year - 1994

Publication title -

communications on pure and applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.12

H-Index - 115

eISSN - 1097-0312

pISSN - 0010-3640

DOI - 10.1002/cpa.3160470205

Subject(s) - mathematics , extension (predicate logic) , eigenvalues and eigenvectors , complex plane , orthogonal polynomials , operator (biology) , matrix (chemical analysis) , polynomial , algebra over a field , pure mathematics , discrete mathematics , combinatorics , mathematical analysis , quantum mechanics , computer science , transcription factor , composite material , gene , programming language , biochemistry , chemistry , physics , materials science , repressor

A new proof of a recent theorem of Ellis, Gohberg, and Lay, which identifies the number of roots of a “continuous” matrix orthogonal polynomial in the open upper halfplane with the number of negative eigenvalues of a related integral operator is presented. A related extension problem is then formulated and solved in assorted classes of functions which are analytic in the open upper half plane, apart from a finite number of poles. A discrete analogue of this extension problem is also formulated and solved. © 1994 John Wiley & Sons, Inc.

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