QWN-EULER OPERATOR AND ASSOCIATED CAUCHY PROBLEM

DOI10.1142/S021902571250004XzbMath1248.60081MaRDI QIDQ2890510

Hafedh Rguigui, Abdessatar Barhoumi, Habib Ouerdiane

Publication date: 11 June 2012

Published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics (Search for Journal in Brave)

zbMATH Keywords

Cauchy problemQWN-derivativesQWN-Euler operator

Mathematics Subject Classification ID

Infinite-dimensional holomorphy (46G20) White noise theory (60H40) Spaces of linear operators; topological tensor products; approximation properties (46A32) Distributions on infinite-dimensional spaces (46F25)

Related Items (13)

Quantum white noise Feynman-Kac formula ⋮ Higher powers of analytical operators and associated ∗-Lie algebras ⋮ Euler's theorem for homogeneous white noise operators ⋮ The q-Gamma White Noise ⋮ Quantum white noise Gaussian kernel operators ⋮ Quantum fractional Ornstein-Uhlenbeck semigroups and associated potentials ⋮ Infinite degrees of freedom Weyl representation: Characterization and application ⋮ Characterization of the \texttt{QWN}-conservation operator and applications ⋮ Quantum white noise stochastic analysis based on nuclear algebras of entire functions ⋮ Quantum \(\lambda\)-potentials associated to quantum Ornstein-Uhlenbeck semigroups ⋮ Quantum Ornstein-Uhlenbeck semigroups ⋮ Operator theory: quantum white noise approach ⋮ QWN-first-order Wick differential operators and an associated transport equation

Cites Work

• Annihilation-derivative, creation-derivative and representation of quantum martingales
• Quantum Laplacian and applications
• Gross Laplacian acting on operators
• Transformation groups on white noise functionals and their applications
• Algebras of operators on holomorphic functions and applications
• Quadratic quantum white noises and Lévy Laplacian.
• A duality theorem between spaces of holomorphic functions of exponential growth
• Quantum Lévy Laplacian and associated heat equation
• Quantum stochastic integral representations of Fock space operators
• QUANTUM EXTENSIONS OF FOURIER-GAUSS AND FOURIER-MEHLER TRANSFORMS
• Transforms on white noise functionals with their applications to Cauchy problems
• QUANTUM STOCHASTIC ANALYSIS VIA WHITE NOISE OPERATORS IN WEIGHTED FOCK SPACE
• UNITARITY OF KUO'S FOURIER–MEHLER TRANSFORM
• ANALYTIC CHARACTERIZATION OF GENERALIZED FOCK SPACE OPERATORS AS TWO-VARIABLE ENTIRE FUNCTIONS WITH GROWTH CONDITION
• Derivations on white noise functionals

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