Related papers: On Pole Placement and Invariant Subspaces
The curious connection between the spacings of the eigenvalues of random matrices and the corresponding spacings of the non trivial zeros of the Riemann zeta function is analyzed on the basis of the geometric dynamical global program of…
By using a real matrix translation, we propose a coupled eigenvalue problem for octonionic operators. In view of possible applications in quantum mechanics, we also discuss the hermiticity of such operators. Previous difficulties in…
Given an arrangement of hyperplanes in $\P^n$, possibly with non-normal crossings, we give a vanishing lemma for the cohomology of the sheaf of $q$-forms with logarithmic poles along our arrangement. We give a basis for the ideal $\cal J$…
We consider the quantum mechanics of a charged particle in the presence of Dirac's magnetic monopole. Wave functions are sections of a complex line bundle and the magnetic potential is a connection on the bundle. We use a continuum…
The present article is devoted to the generalized Salem functions, the generailed shift operator, and certain related problems. A description of further investigations of the author of this article is given.These investigations (in terms of…
This paper studies eigenvalues of the buckling problem of arbitrary order on bounded domains in Euclidean spaces and spheres. We prove universal bounds for the k-th eigenvalue in terms of the lower ones independent of the domains. Our…
The article $-$ part of a larger thesis which aims to give a detailed description of the generalisation to the category of groups with operators of the classical theory of semisimplicity for modules $-$ presents a straightforward…
Interpretations of the Beurling-Lax-Halmos Theorem on invariant subspaces of the unilateral shift are explored using the language of Hilbert modules. Extensions and consequences are considered in both the one and multivariate cases with an…
Standard perturbation theory of eigenvalue problems consists of obtaining approximations of eigenmodes in the neighborhood of an operator where the corresponding eigenmode is known. Nevertheless, if the corresponding eigenmodes of several…
This note revisits some majorization inequalities for eigenvalues, special attention is given to an elegant theorem of Hiroshima. An extension of the special case of Hiroshima's theorem is presented. Some discussion and open problems are…
In this paper, we propose a decomposition approach for eigenvalue problems with spatial symmetries, including the formulation, discretization as well as implementation. This approach can handle eigenvalue problems with either Abelian or…
Standard subspaces are closed real subspaces of a complex Hilbert space that appear naturally in Tomita-Takesaki modular theory and its applications to quantum field theory. In this article, inclusions of standard subspaces are studied…
We study a parabolic initial-boundary-value problem for a system of two differential equations with two boundary conditions of different orders, the Dirichlet and Neumann ones. It occurs specifically in the heat-mass transfer theory. We…
We exhibit algorithms to compute systems of Hecke eigenvalues for spaces of Hilbert modular forms over a totally real field. We provide many explicit examples as well as applications to modularity and Galois representations.
We first propose a generalization of the notion of Mathieu subspaces of associative algebras $\mathcal A$, which was introduced recently in [Z4] and [Z6], to $\mathcal A$-modules $\mathcal M$. The newly introduced notion in a certain sense…
We obtain a second order differential equation on moduli space satisfied by certain modular graph functions at genus two, each of which has two links. This eigenvalue equation is obtained by analyzing the variations of these graphs under…
We give a formula for pushing forward the classes of Hall-Littlewood polynomials in Grassmann bundles, generalizing Gysin formulas for Schur S- and Q-functions.
A general theory of vector-valued modular functions, holomorphic in the upper half-plane, is presented for finite dimensional representations of the modular group. This also provides a description of vector-valued modular forms of arbitrary…
This paper provides insights into the role of symmetry in studying polynomial functions vanishing to high order on an algebraic variety. The varieties we study are singular loci of hyperplane arrangements in projective space, with emphasis…
For a simple and connected graph, a new graph invariant $s_{\alpha}^{*}(G)$, defined as the sum of powers of the eigenvalues of the normalized Laplacian matrix, has been introduced by Bozkurt and Bozkurt in [7]. Lower and upper bounds have…