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Quantum Heat Equation with Quantum K-Gross Laplacian: Solutions and Integral Representation
Conference proceeding

Quantum Heat Equation with Quantum K-Gross Laplacian: Solutions and Integral Representation

Samah Horrigue and Habib Ouerdiane
QUANTUM PROBABILITY AND INFINITE DIMENSIONAL ANALYSIS, Vol.25, pp.185-202
QP-PQ Quantum Probability and White Noise Analysis
01/01/2010
DOI: https://doi.org/10.1142/9789814295437_0013

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology Statistics & Probability
In this paper, we first introduce and study the quantum (K-1, K-2)-Gross Laplacian denoted Delta(QG)(K-1, K-2). Then, we prove that Delta(QG)(K-1, K-2) is a well defined and linear continuous operator acting on the space of continuous operators and has a quantum stochastic integral. Finally, we give an explicit solution of the quantum heat equation associated with Delta(QG)(K-1, K-2). Then, under some positive conditions, we give an integral representation of this solution.

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