Paradan’s wall crossing formula for partition functions and Khovanski-Pukhlikov differential operator

Paradan’s wall crossing formula for partition functions and Khovanski-Pukhlikov differential operator

Wall rational functions and Khrushchev’s formula for orthogonal rational functions

We prove that the Nevalinna-Pick algorithm provides different homeomorphisms between certain topological spaces of measures, analytic functions and sequences of complex numbers. This algorithm also yields a continued fraction expansion of every Schur function, whose approximants are identified. The approximants are quotients of rational functions which can be understood as the rational analogs ...

Bi-concave Functions Defined by Al-Oboudi Differential Operator

The purpose of the present paper is to introduce a class $D_{Sigma ;delta }^{n}C_{0}(alpha )$ of bi-concave functions defined by Al-Oboudi differential operator. We find estimates on the Taylor-Maclaurin coefficients $leftvert a_{2}rightvert $ and $leftvert a_{3}rightvert$ for functions in this class. Several consequences of these results are also pointed out in the form of corollaries.

Krein’s Trace Formula for Unitary Operators and Operator Lipschitz Functions

The spectral shift function for pairs of selfadjoint operators was introduced in the paper by I.M. Lifshits [17]. In the same paper a trace formula for the difference of functions of the perturbed operator and the unperturbed operator was established. Ideas by Lifshits were developed in the paper by M.G. Krein [14], in which the spectral shift function ξ in L1(R) was defined for arbitrary pairs...

Strong differential subordination and superordination of analytic functions associated with Komatu operator

Strong dierential subordination and superordination properties are determined for some familiesanalytic functions in the open unit disk which are associated with the Komatu operator by investigatingappropriate classes of admissible functions. New strong dierential sandwich-type results arealso obtained.