Transformations of Wiener integrals under a general class of linear transformations

On One-Sided Ideals of Rings of Linear Transformations

Approximation of a Class of Wiener Integrals*

and since evaluation of this integral by analysis often cannot be done, it is of some practical interest to investigate the possibility of numerically evaluating this integral. Such a calculation is expected to require an enormous amount of arithmetic since it involves the evaluation of a fc-fold integral where k >5> 1 ; an exact evaluation requires going to the limit k —* ». Consequently, it i...

Transformations of hypergeometric elliptic integrals

The paper classifies algebraic transformations of Gauss hypergeometric functions with the local exponent differences (1/2, 1/4, 1/4), (1/2, 1/3, 1/6) and (1/3, 1/3, 1/3). These form a special class of algebraic transformations of Gauss hypergeometric functions, of arbitrary high degree. The Gauss hypergeometric functions can be identified as elliptic integrals on the genus 1 curves y = x − x or...

Transformations of elliptic hypergeometric integrals

We prove a pair of transformations relating elliptic hypergeometric integrals of different dimensions, corresponding to the root systems BCn and An; as a special case, we recover some integral identities conjectured by van Diejen and Spiridonov. For BCn, we also consider their “Type II” integral. Their proof of that integral, together with our transformation, gives rise to pairs of adjoint inte...

A Characterization of the Entropy--Gibbs Transformations

Let h be a finite dimensional complex Hilbert space, b(h)+ be the set of all positive semi-definite operators on h and Phi is a (not necessarily linear) unital map of B(H) + preserving the Entropy-Gibbs transformation. Then there exists either a unitary or an anti-unitary operator U on H such that Phi(A) = UAU* for any B(H) +. Thermodynamics, a branch of physics that is concerned with the study...