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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 11, pp. 1498–1511, November, 2015.
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Lopushans’kyi, O.V., Sharyn, S.V. Application of the Laplace Transform of Tempered Distributions to the Construction of Functional Calculus. Ukr Math J 67, 1687–1703 (2016). https://doi.org/10.1007/s11253-016-1183-8
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DOI: https://doi.org/10.1007/s11253-016-1183-8