A product integral representation for an evolution system

An analytic double product integral

The double product integral →← ∏ (1+λ(dA†⊗dA−dA⊗dA†)) is constructed as a family of unitary operators in double Fock space satisfying quantum stochastic differential equations with unbounded operator coefficients.

A representation scheme for digital product service system definitions

http://dx.doi.org/10.1016/j.aei.2014.07.004 1474-0346/ 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/3.0/). ⇑ Corresponding author. Tel.: +44 113 343 2113. E-mail addresses: [email protected] (A. McKay), [email protected] (S. Kundu). 1 Present address: School of Engineering, Manchester Metropolitan U...

An Integral Evolution Formula for theWave Equation

An Integral Evolution Formula for the Wave Equation Bradley Alpert,∗,1 Leslie Greengard,†,2 and Thomas Hagstrom‡,3 ∗National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80303,†Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012-1110, and ‡Department of Mathematics and Statistics, University of New Mexico, Albuqu...

A Design For An Islamic Economic System

Admissible Vectors of a Covariant Representation of a Dynamical System

In this paper, we introduce admissible vectors of covariant representations of a dynamical system which are extensions of the usual ones, and compare them with each other. Also, we give some sufficient conditions for a vector to be admissible vector of a covariant pair of a dynamical system.  In addition, we show the existence of Parseval frames for some special subspaces of $L^2(G)$ related to...