GENERALIZED WEINSTEIN AND SOBOLEV SPACES

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2021 by IJMTT Journal
Volume-67 Issue-3
Year of Publication : 2021
Authors : HASSEN BEN MOHAMED, MOHAMED MOKTAR CHAFFAR
  10.14445/22315373/IJMTT-V67I3P505

MLA

MLA Style: HASSEN BEN MOHAMED, MOHAMED MOKTAR CHAFFAR "GENERALIZED WEINSTEIN AND SOBOLEV SPACES" International Journal of Mathematics Trends and Technology 67.3 (2021):28-44. 

APA Style: HASSEN BEN MOHAMED, MOHAMED MOKTAR CHAFFAR(2021). GENERALIZED WEINSTEIN AND SOBOLEV SPACES International Journal of Mathematics Trends and Technology, 28-44.

Abstract
In this paper we present a brief history and the basic ideas of the generalized Weinstein operator ΔWα,d,n which generalizes the Weinstein operator ΔWα,d,n. In n=0 we regain the Weinstein operator has several applications in pure and applied mathematics especially in fluid mechanics. We study the Sobolev spaces of exponential type Hsα,n(R+d+1) associated with the generalized Weinstein and investigate their properties, Sobolev spaces are named after the Russian mathematician Sergei Sobolev. Using the theory of reproducing kernels ( which was written in 1942-1943), we introduce a class of symbols of exponential type and their associated pseudo differential operators related to the generalized Weinstein operator ΔWα,d,n and finally, we give some applications to these spaces.

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Keywords : Sobolev Spaces, Generalized Weinstein operator, Generalized Weinstein transform, Weinstein, Kernel Reproducing Theory, pseudodifferential operator.