Boundary Values and Convolution in Ultradistribution Spaces

Gelfand–Shilov Type Spaces Through Hermite Expansions

“…This result was obtained by Kashpirovskii [5] and later by other authors, cf [2]. In addition it holds…”

“…Gelfand-Shilov spaces S α (R d ), S β (R d ) and S β α (R d ) and their generalisations, the Gelfand-Shilov spaces of Roumieau and Beuerling type S {Mp} (R d ) respectivly S (Mp) (R d ) are discussed in [2], [3], [4], [6], [7], [9], [10], [11] and [12]. In this paper we focus on the special cases S β α (R d ), resp., β α (R d ).…”

Eigenfunction expansions of ultradifferentiable functions and ultradistributions

“…Regularity properties of spaces of ultradistributions have been studied by Pilipović and Scarpalezos [PS01]. We can refer to a relatively recent book by Carmichael, Kamiński and Pilipović [CKP07] for more details on these and other properties of ultradistributions on R n and related references. The paper is organised as follows.…”

Ultradistributional boundary values of harmonic functions on the sphere

“…There is a vast literature dealing with boundary values on R n , see e.g. [1,5,6,10,12,14,20] and references therein. In the case of the unit sphere S n−1 , the characterization of harmonic functions in the Euclidean unit ball of R n having distributional boundary values on S n−1 was given by Estrada and Kanwal in [11].…”