Abstract
Publisher Summary This chapter focuses on some degenerated differential operators on vector bundles; and discusses the notation of the mathematical concepts that are used in the described differential operators, and relations between the class of these differential operators and infinitesimal generators of semigroups of operators. It discusses k-th order differential operator, some auxiliary spaces, Hilbert space, Riemannian structure, the sesqui-linear form, a family of continuous sesquil-linear forms, bijections associated with certain differential operator, analytic theory of semi-groups of operators, method for the construction of semi-groups, Hermitian structure, various theorems, and lemmas.
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