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By Yu.M. Berezansky,A.A. Kalyuzhnyi

First works relating to the themes coated during this booklet belong to J. Delsarte and B. M. Le­ vitan and seemed due to the fact that 1938. In those works, the households of operators that generalize traditional translation operators have been investigated and the corresponding harmonic research used to be built. Later, ranging from 1950, it was once spotted that, in such buildings, a tremendous function is performed by way of the truth that the kernels of the corresponding convolutions of capabilities are nonnegative and through the houses of the normed algebras generated by way of those convolutions. That used to be the way in which the proposal of hypercomplex procedure with continu­ ous foundation seemed. A hypercomplex procedure is a normed algebra of services on a in the neighborhood compact house Q-the "basis" of this hypercomplex method. Later, comparable gadgets, hypergroups, have been brought, that have complex-valued measures on Q as parts and convolution outlined to be basically the convolution of functionals and twin to the unique convolution (if measures are considered as functionals at the area of continuing services on Q). besides the fact that, till 1991, the time while this publication was once written in Russian, there have been no monographs containing basics of the idea (with an exception of a quick part within the ebook by way of Yu. M. Berezansky and Yu. G. Kondratiev [BeKo]). The authors desired to provide an advent to the speculation and canopy crucial next effects and examples.

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Harmonic Analysis in Hypercomplex Systems (Mathematics and Its Applications) by Yu.M. Berezansky,A.A. Kalyuzhnyi

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