Heine Representations And Monotonicity Properties Of Determinants And Pfaffians

Keywords

Absolute monotonicity; Complete monotonicity; Determinant; Orthogonal functions; Pfaffian

Abstract

We establish integral representations of Heine type for certain integrals of determinants. We use these representations to derive monotonicity properties of such determinants. New integral representations of Heine type for biorthogonal functions obtained from the general Gram–Schmidt orthonormalization process are given. We also establish the monotonicity of certain Pfaffians using the de Bruijn formula of Ishikawa and Zeng. The complete or absolute monotonicity of a number of Pfaffian functions is established.

Publication Date

4-1-2015

Publication Title

Constructive Approximation

Volume

41

Issue

2

Number of Pages

231-249

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s00365-014-9262-2

Socpus ID

84923846475 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84923846475

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