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Ehssan Khanmohammadi

Publications and source records attributed to Ehssan Khanmohammadi.

4 recordsLinked to original sources
arXiv2020

From Uniform Boundedness to the Boundary Between Convergence and Divergence

In this article we introduce a dual of the uniform boundedness principle which does not require completeness and gives an indirect means for testing the boundedness of a set. The dual principle, although known to the analyst and despite its applications in establishing results such as Hellinger--Toeplitz theorem, is often missing from elementary treatments of functional analysis. In Example 1 we indicate a connection between the dual principle and a question in spirit of du Bois-Reymond regarding the boundary between convergence and divergence of sequences. This example is intended to illustrate why the statement of the principle is natural and clarify what the principle claims and what it does not.

math.FA↗
arXiv2020

On the Positivity of Kirillov's Character Formula

We give a direct proof for the positivity of Kirillov's character on the convolution algebra of smooth, compactly supported functions on a connected, simply connected nilpotent Lie group $G$. Then we use this positivity result to construct a representation of $G\times G$ and establish a $G\times G$-equivariant isometric isomorphism between our representation and the Hilbert--Schmidt operators on the underlying representation of $G$. In fact, we provide a more general framework in which we establish the positivity of Kirillov's character for coadjoint orbits of groups such as $\operatorname{SL}(2, \mathbb{R})$ under additional hypotheses that are automatically satisfied in the nilpotent case. These hypotheses include the existence of a real polarization and the Pukanzsky condition.

math.RT↗
arXiv2016

A Structured Inverse Spectrum Problem For Infinite Graphs

It is shown that for a given infinite graph $G$ on countably many vertices, and a compact, infinite set of real numbers $Λ$ there is a real symmetric matrix $A$ whose graph is $G$ and its spectrum is $Λ$. Moreover, the set of limit points of $Λ$ equals the essential spectrum of $A$, and the isolated points of $Λ$ are eigenvalues of $A$ with multiplicity one. It is also shown that any two such matrices constructed by our method are approximately unitarily equivalent.

math.SP↗