Related papers: Notes on the sin2\Theta\ theorem

Fuglede-Putnam Theorem have been proved for a considerably large number of class of operators. In this paper by using the spectral theory, we obtain a theoretical and general framework from which Fuglede-Putnam theorem may be promptly…

We establish the small data solvability of suitable quasilinear wave and Klein-Gordon equations in high regularity spaces on a geometric class of spacetimes including asymptotically de Sitter spaces. We obtain our results by proving the…

On the half line $[0,\infty)$ we study first order differential operators of the form $B 1/i d/(dx) + Q(x)$, where $B:=\mat{B_1}{0}{0}{-B_2}$, $B_1,B_2\in M(n,\C)$ are self--adjoint positive definite matrices and $Q:\R_+\to M(2n,\C)$,…

We introduce a comprehensive framework for subordinacy theory applicable to long-range operators on $\ell^2(\mathbb Z)$, bridging dynamical systems and spectral analysis. For finite-range operators, we establish a correspondence between the…

In part II we constructed the lower bound, in the spirit of $\Gamma$- $\liminf$ for some general classes of singular perturbation problems, with or without the prescribed differential constraint, taking the form E_\e(v):=\int_\Omega…

We consider small nonlinear perturbations of linear systems on a time scale with the phase space being finite or infinite-dimensional. For $\Delta$-differential operators, corresponding to linear dynamic systems we consider their…

We prove some general Sobolev-Orlicz, Nash and Faber-Krahn inequalities for positive operators of given ultracontractive norms of the spectral projectors on ]0, lambda]. For invariant operators on coverings of finite simplicial complexes…

For p-subordinate perturbations of unbounded normal operators, the change of the spectrum is studied and spectral criteria for the existence of a Riesz basis with parentheses of root vectors are established. A Riesz basis without…

The ground state of the $\SO(2n)_{1} \times \SO(2n)_{1} \over \SO(2n)_{2}$ coset theories, perturbed by the $\phi^{id,id}_{adj}$ operator and those of the sine-Gordon theory, for special values of the coupling constant in the attracting…

The primary objective of this paper is to generalize the results of [arXiv:2111.03548] to the case of quasi-smooth Berkovich curves by establishing a connection between the spectrum and the radii of convergence. To achieve this, we…

Let $\gH$ be a Hilbert space and let $A$ be a simple symmetric operator in $\gH$ with equal deficiency indices $d:=n_\pm(A)<\infty$. We show that if, for all $\l$ in an open interval $I\subset\bR$, the dimension of defect subspaces…

In this work, we consider Dirac-type operators with a constant delay less than half of the interval and not less than two-fifths of the interval. For our considered Dirac-type operators, two inverse spectral problems are studied.…

A discrepancy principle for solving nonlinear equations with monotone operators given noisy data is formulated. The existence and uniqueness of the corresponding regularization parameter $a(\delta)$ is proved. Convergence of the solution…

For the inclusion problem involving two maximal monotone operators, under the metric subregularity of the composite operator, we derive the linear convergence of the generalized proximal point algorithm and several splitting algorithms,…

The extended Davis-Kahan theorem makes use of polynomial matrix transformations to produce bounds at least as tight as the standard Davis-Kahan theorem. The optimization problem of finding transformation parameters resulting in optimal…

We show that single-valuation exponential kernels, under mild regularity assumptions, converge in the continuum limit to a fourth-order operator with heat asymptotics $\Theta(t)\sim t^{-1/4}$ and hence spectral dimension $d_s=\tfrac12$.…

In this paper we establish an improvement of tilt-excess decay estimate for the Allen-Cahn equation, and use this to give a new proof of Savin's theorem on the uniform $C^{1,\alpha}$ regularity of flat level sets, which then implies the one…

We construct a functional model for rank one perturbations of compact normal operators acting in a certain Hilbert spaces of entire functions generalizing de Branges spaces. Using this model we study completeness and spectral synthesis…

The operator of double differentiation, perturbed by the composition of the differentiation operator and a convolution one, on a finite interval with Dirichlet boundary conditions is considered. We obtain uniform stability of recovering the…

The unitary transformation of path-integral differential measure is described. The main properties of perturbation theory in the phase space of action-angle, energy-time variables are investigated. The measure in cylindrical coordinates is…