Related papers: Extended resolvent of heat operator with multisoli…
We consider the resolvent of a system of first order differential operators with a regular singularity, admitting a family of self-adjoint extensions. We find that the asymptotic expansion for the resolvent in the general case presents…
In this paper we estimate norms of integral operator induced with Green function related to the Poisson equation in the unit ball with vanishing boundary data.
We study a second-order parabolic equation with divergence form elliptic operator, having piecewise constant diffusion coefficients with two points of discontinuity. Such partial differential equations appear in the modelization of…
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…
We prove a variant of Krein's resolvent formula expressing the resolvents of self-adjoint extensions through the associated boundary conditions. Applications to solvable quantum-mechanical problems are discussed.
In a companion paper, we derived analytical expressions for the structure factor of the square-shoulder potential in a perturbative way around the high- and low-temperature regimes. Here, various physical properties of these solutions are…
It is shown that multisoliton solutions of several well known nonlinear PDEs(x, t) can be obtained by certain separation of variables: each n-soliton arises from a mutual solution of a nonlinear ODE(x), common for all NPDEs considered, and…
We develop heat kernel and Green's function estimates for manifolds with positive bottom spectrum. The results are then used to establish existence and sharp estimates of the solution to the Poisson equation on such manifolds with Ricci…
The mathematical properties associated with the widely accepted concept of the extensivity of many of the common thermodynamic variables are examined and some of their consequences considered. The possible conflict between some of these and…
Using the formalism of extended $N=4$ supersymmetric quantum mechanics we consider the procedure of the construction of multi--well potentials. We demostrate the form--invariance of Hamiltonians entering the supermultiplet, using the…
A multivariable version of the strong maximal function is introduced and a sharp distributional estimate for this operator in the spirit of the Jessen, Marcinkiewicz, and Zygmund theorem is obtained. Conditions that characterize the…
Modeling quantum thermal machines provides a practical approach to describing the thermodynamic properties of quantum technologies and devices. For this purpose, power-law potentials are often employed as working mediums of quantum…
We study spectral properties of the Schroedinger operator with an imaginary sign potential on the real line. By constructing the resolvent kernel, we show that the pseudospectra of this operator are highly non-trivial, because of a blow-up…
We prove the existence of sectors of minimal growth for general closed extensions of elliptic cone operators under natural ellipticity conditions. This is achieved by the construction of a suitable parametrix and reduction to the boundary.…
We bring together two apparently disconnected lines of research (of mathematical and of physical nature, respectively) which aim at the definition, through the corresponding zeta function, of the determinant of a differential operator…
We deal with the boundedness properties of higher order commutators related to some generalizations of the multilinear fractional integral operator of order $m$, $I_\alpha ^m$, from a product of weighted Lebesgue spaces into adequate…
We consider two-dimensional Schroedinger operators with magnetic field. Under certain regularity and decay assumptions on the magnetic and electric field we show that the behavior of the corresponding resolvent at threshold and the behavior…
A quantum field described by the field operator $\Delta_{a}=\Delta+ a\delta_\Sigma$ involving a $\delta$-like potential is considered. Mathematically, the treatment of the $\delta$-potential is based on the theory of self-adjoint extension…
We give examples of semiclassical Schr\"odinger operators with exponentially large cutoff resolvent norms, even when the supports of the cutoff and potential are very far apart. The examples are radial, which allows us to analyze the…
First, we briefly review the conditions under which the entropy $S_q$ can be extensive (Tsallis, Gell-Mann and Sato, Proc. Natl. Acad. Sc. USA (2005), in press; cond-mat/0502274), as well as the possible $q$-generalization of the central…