Related papers: On polynomials in spectral projections of spin ope…

We study the behaviour of the conformal block expansions of scalar fivepoint Lorentzian conformal correlators in the limit where multiple cross ratios approach zero. Since this limit is controlled by intermediate operators with large spin,…

In this paper, bivariate Szasz-Mirakjan type operators are introduced along with the estimation of its approximation properties and its rate of convergence. Furthermore, to check the asymptotic behavior of the said bivariate operators, the…

Let X_N= (X_1^(N), ..., X_p^(N)) be a family of N-by-N independent, normalized random matrices from the Gaussian Unitary Ensemble. We state sufficient conditions on matrices Y_N =(Y_1^(N), ..., Y_q^(N)), possibly random but independent of…

A new approach to normal operators in real Hilbert spaces is discussed, and a spectral representation is obtained, derived directly from the complex case. The results are then applied to quaternionic normal operators, regarded as a special…

Some properties and relations satisfied by the polynomial solutions of the bispectral problem are studied. Given a differential operator, under certain restrictions its polynomial eigenfunctions are explicitly obtained, as well as the…

For relatively form-compact perturbations of non-negative selfadjoint operators, we obtain an upper bound on the number of discrete eigenvalues in half-planes separated from the positive real axis. The bound is given in terms of a partial…

We consider the spectrum of a two-dimensional Pauli operator with a compactly supported electric potential and a variable magnetic field with a positive mean value. The rate of accumulation of eigenvalues to zero is described in terms of…

This note discusses how an operator analog of the Lagrange polynomial naturally arises in the quantum-mechanical problem of constructing an explicit form of the spin projection operator.

In this note we show how improved $L^p$-estimates for certain types of quasi-modes are naturally equaivalent to improved operator norms of spectral projection operators associated to shrinking spectral intervals of the appropriate scale.…

This article is devoted to the spectral analysis of the electro-magnetic Schr\"odinger operator on the Euclidean plane. In the semiclassical limit, we derive a pseudo-differential effective operator that allows us to describe the spectrum…

The relation between the spectral decomposition of a self-adjoint operator which is realizable as a higher order recurrence operator and matrix-valued orthogonal polynomials is investigated. A general construction of such operators from…

For polynomials in independent Wigner matrices, we prove convergence of the largest singular value to the operator norm of the corresponding polynomial in free semicircular variables, under fourth moment hypotheses. We actually prove a more…

We prove the long standing conjecture in the theory of two-point boundary value problems that completeness and Dunford's spectrality imply Birkhoff regularity. In addition we establish the even order part of S.G.Krein's conjecture that…

We study the spectrum of operators in the Schwartz space of rapidly decreasing functions which associate each function with its composition with a polynomial. In the case where this operator is mean ergodic we prove that its spectrum…

In this paper we show variant of the spectral theorem using an algebraic Jordan-Schwinger map. The advantage of this approach is that we don't have restriction of normality on the class of operators we consider. On the other side, we have…

We build a combinatorial invariant, called the spectral monodromy from the spectrum of a non-selfadjoint h -pseudodifferential operator with two degrees of freedom in the semi-classical limit. We treat small non-selfadjoint perturbation of…

In this paper we study the subdifferential set of an operator. We give possible relation of the subdifferential set of an operator to that of its value, at a point where the operator attains its norm.

A family of spectral decompositions of the spin-weighted spheroidal wave operator is constructed for complex aspherical parameters with bounded imaginary part. As the operator is not symmetric, its spectrum is complex and Jordan chains may…

The variation of spectral subspaces for linear self-adjoint operators under an additive bounded perturbation is considered. The objective is to estimate the norm of the difference of two spectral projections associated with isolated parts…

The purpose of this note is to investigate the concentration properties of spectral projectors on manifolds. This question has been intensively studied (by Logvinenko--Sereda, Nazarov, Jerison--Lebeau, Kovrizhkin,…