2017
Том 69
№ 6

All Issues

Application of the Laplace Transform of Tempered Distributions to the Construction of Functional Calculus

Lopushanskyi A. O., Sharyn S. V.


Abstract

We use the generalized n-dimensional Laplace transform of tempered distributions whose supports are located in a positive n-dimensional cone to construct functional calculus for the commutative collections of injective generators of n-parameter analytic semigroups of operators acting in a Banach space.

English version (Springer): Ukrainian Mathematical Journal 67 (2015), no. 11, pp 1687-1703.

Citation Example: Lopushanskyi A. O., Sharyn S. V. Application of the Laplace Transform of Tempered Distributions to the Construction of Functional Calculus // Ukr. Mat. Zh. - 2015. - 67, № 11. - pp. 1498-1511.