Application of the Laplace Transform of Tempered Distributions to the Construction of Functional Calculus - Lopushanskyi, A. O.; Sharyn, S. V. (Ukrains’kyi Matematychnyi Zhurnal, 2015)
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.