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Generalization of the Heyde Theorem to Some Locally Compact Abelian Groups
According to the well-known Heyde theorem, the Gaussian distribution on the real line is characterized by the symmetry of the conditional...
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Structure of the Semi-group of Regular Probability Measures on Locally Compact Hausdorff Topological Semiroups
Let G be a locally compact Hausdorff semi-group, and \(P\left( G\right) \)...
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Witten deformation on non-compact manifolds: heat kernel expansion and local index theorem
Asymptotic expansions of heat kernels and heat traces of Schrödinger operators on non-compact spaces are rarely explored, and even for cases as...
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Compact Sobolev embeddings on non-compact manifolds via orbit expansions of isometry groups
Given a complete non-compact Riemannian manifold ( M , g ) with certain curvature restrictions, we introduce an expansion condition concerning a group...
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Point processes, cost, and the growth of rank in locally compact groups
Let G be a locally compact, second countable, unimodular group that is nondiscrete and noncompact. We explore the ergodic theory of invariant point...
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Estimating Chord-Dot-Normal SIO’s on Domains with Compact Boundaries
In this section we shall embark on a study aimed at clarifying of how the flatness of a “surface” is related to the functional analytic properties of...
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Heyde Theorem for Locally Compact Abelian Groups Containing No Subgroups Topologically Isomorphic to the 2-Dimensional Torus
We prove the following group analogue of the well-known Heyde theorem on a characterization of the Gaussian distribution on the real line. Let X be a...
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COMPACT OPERATORS
This chapter recalls various elementary facts about compact operators. We prove the fundamental fact that...
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Evolutionary equations are G-compact
We prove a compactness result related to G -convergence for autonomous evolutionary equations in the sense of Picard. Compared to previous work...
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The fractional Schrödinger equation on compact manifolds: global controllability results
The goal of this work is to prove global controllability and stabilization properties for the fractional Schrödinger equation on d -dimensional...
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Compact Groups
In this chapter the simply connected groups which are universal coverings of compact groups are studied. It is proved that the Lie algebra...
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Existence of minimizers for causal variational principles on compact subsets of momentum space in the homogeneous setting
We prove the existence of minimizers for the causal action in the class of negative definite measures on compact subsets of momentum space in the...