Complex Analysis and Operator Theory

, Volume 12, Issue 7, pp 1637–1656 | Cite as

Characterization Theorems for the Quantum White Noise Gross Laplacian and Applications

  • Hafedh RguiguiEmail author


This paper reports on the characterization of the quantum white noise (QWN) Gross Laplacian based on nuclear algebra of white noise operators acting on spaces of entire functions with \(\theta \)-exponential growth of minimal type. First, we use extended techniques of rotation invariance operators, the commutation relations with respect to the QWN-derivatives and the QWN-conservation operator. Second, we employ the new concept of QWN-convolution operators. As application, we study and characterize the powers of the QWN-Gross Laplacian. As for their associated Cauchy problem it is solved using a QWN-convolution and Wick calculus.


QWN-Gross Laplacian QWN-convolution operators Rotation invariance operators Wick product Cauchy problem 

Mathematics Subject Classification

Primary 60H40 Secondary 46A32 46F25 46G20 


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Copyright information

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Authors and Affiliations

  1. 1.Department of Mathematics, High School of Sciences and Technology of Hammam SousseUniversity of SousseHammam SousseTunisia
  2. 2.Department of MathematicsAL-Qunfudhah University college, Umm Al-Qura UniversityMeccaSaudi Arabia

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