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Wick differential and Poisson equations associated to the πš€πš†π™½-Euler operator acting on generalized operators

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Published/Copyright: December 30, 2016
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 66 Issue 6

Abstract

In this paper we study the homogeneous Wick differential equation associated to the quantum white noise (πš€πš†π™½) Euler operator Ξ”Eg,Q acting on generalized operators. Ξ”Eg,Q is defined as sum of the extension of the πš€πš†π™½-Gross Laplacian and the πš€πš†π™½-conservation operator. It is shown that the operator Ξ”Eg,Q has a representation in terms of the πš€πš†π™½-derivatives {Dcβˆ’,Dc+:c∈N}. The poisson equation is worked out as a non homogeneous Wick differential equation associated to Ξ”Eg,Q.

MSC 2010: Primary 60H40; 46A32; 46F25; 46G20
Keywords: Wick differential equation; πš€πš†π™½-Gross Laplacian; πš€πš†π™½-conservation operator; πš€πš†π™½-Euler operator; Poisson equation
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(Communicated by Sylvia PulmannovΓ‘)

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Received: 2014-6-9
Accepted: 2014-11-11
Published Online: 2016-12-30
Published in Print: 2016-12-1

Β© 2016 Mathematical Institute Slovak Academy of Sciences

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  16. On approximation of functions by some hump matrix means of Fourier series
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  32. On the internal approach to differential equations 3. Infinitesimal symmetries
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https://doi.org/10.1515/ms-2016-0238
Keywords for this article
Wick differential equation; πš€πš†π™½-Gross Laplacian; πš€πš†π™½-conservation operator; πš€πš†π™½-Euler operator; Poisson equation

Articles in the same Issue

  2. A triple representation of lattice effect algebras
  4. Periods of morgan-voyce sequences and elliptic curves
  6. Multiplicative generalized derivations on ideals in semiprime rings
  8. A few remarks on PoincarΓ©-Perron solutions and regularly varying solutions
  10. Applications of extremal theorem and radius equation for a class of analytic functions
  12. On the β€œbang-bang” principle for a class of Riemann-Liouville fractional semilinear evolution inclusions
  14. New criteria for global exponential stability of linear time-varying volterra difference equations
  16. On approximation of functions by some hump matrix means of Fourier series
  18. Pseudo-amenability and pseudo-contractibility for certain products of Banach algebras
  20. Poisson kernels on semi-direct products of abelian groups
  22. Locally convex projective limit cones
  24. On the properties (wL) and (wV)
  26. On the existence of solutions for quadratic integral equations in Orlicz spaces
  28. Existence and uniqueness of best proximity points under rational contractivity conditions
  30. Almost Weyl structures on null geometry in indefinite Kenmotsu manifolds
  32. On the internal approach to differential equations 3. Infinitesimal symmetries
  34. A Characterization of the discontinuity point set of strongly separately continuous functions on products
  36. Wick differential and Poisson equations associated to the πš€πš†π™½-Euler operator acting on generalized operators
  38. Multivariate EIV models
  40. On codes over 𝓑k, m and constructions for new binary self-dual codes
  42. Domination number of total graphs
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