International Journal of Mathematics Trends and Technology
Volume 67 | Issue 3 | Year 2021 | Article Id. IJMTT-V67I3P505 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I3P505
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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HASSEN BEN MOHAMED, "GENERALIZED WEINSTEIN AND SOBOLEV SPACES," International Journal of Mathematics Trends and Technology (IJMTT), vol. 67, no. 3, pp. 28-44, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I3P505
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