An algebraic approach to tempered ultradistributions
The presentation of an isomorphism between the space of tempered distributions and that of pseudo-quotients associated with their convergence structures in [\textit{D.~Atanasiu} et al., J. Math. Anal. Appl. 384, No.~2, 307--319 (2011; Zbl 1230.42013)] inspired the authors to furnish such a result for the Beurling tempered ultradistribution spaces. The theme of the system of investigation remains the same as that in [loc. cit.], however, the analysis made to obtain the results is entirely different in the sense that in this paper an intrinsic analysis of a class of ultradistributional operators is employed instead. Let \(M\) denote the space of all functions of sub-exponential growth, which is a vector space closed under multiplication by ultrapolynomials of the form given by Equation (1.4) in the paper. An estimation for \(M_p\) polynomials is given later.
ultradifferentiable functions of ultrapolynomial growth
scientific article; zbMATH DE number 6897102