相关论文: The generalized Saint Venant operator and integral…

A collection of infinite dimensional complete vector fields $\left\{V_i\right\}_{i=1}^{\infty}$ acting on a locally convex manifolds $M$ on which a smooth positive measure $\mu$ is defined was considered. It was assumed that the vector…

We give a new class of equivalent norms for modulation spaces by replacing the window of the short-time Fourier transform by a Hilbert-Schmidt operator. The main result is applied to Cohen's class of time-frequency distributions, Weyl…

We establish an equivalence principle between the solenoidal injectivity of the geodesic ray transform acting on symmetric $m$-tensors and the existence of invariant distributions or smooth first integrals with prescribed projection over…

In the present paper, we study quantum Sobolev spaces whose elements are operators of the Hilbert-Schmidt class. We construct these Sobolev spaces from the Fourier transform for operators. Next, we obtain continuous embedding theorems.…

We give a complete classification in canonical forms on finite-dimensional vector spaces over the real numbers.

A generalized covariant method of analysis applicable to frames for which time is not orthogonal to space, such as spacetime around a star possessing angular momentum or on a rotating disk, is presented. Important aspects of such an…

We generalize the approach to localization in one dimension introduced by Kunz-Souillard, and refined by Delyon-Kunz-Souillard and Simon, in the early 1980's in such a way that certain correlations are allowed. Several applications of this…

We generalize the definition of convolution of vectors and tensors on the 2-sphere, and prove that it commutes with differential operators. Moreover, vectors and tensors that are normal/tangent to the spherical surface remain so after the…

We study singular Schr\"odinger operators on a finite interval as selfadjoint extensions of a symmetric operator. We give sufficient conditions for the symmetric operator to be in the $n$-entire class, which was defined in our previous…

Path integral representations for generalized Schr\"odinger operators obtained under a class of Bernstein functions of the Laplacian are established. The one-to-one correspondence of Bernstein functions with L\'evy subordinators is used,…

We consider a generalization of a duality symmetric model proposed by Schwarz and Sen. It is based on enlarging the model with a dynamical vector field being a time-like component of a local Lorentz frame. This allows one to preserve the…

The factorisation method for Schr\"odinger operators with magnetic fields on a two-dimensional surface $M^2$ with non-trivial metric is investigated. This leads to the new integrable examples of such operators and brings a new look at some…

We construct a special class of semiclassical Fourier integral operators whose wave fronts are symplectic micromorphisms. These operators have very good properties: they form a category on which the wave front map becomes a functor into the…

In this paper, we introduce the Theta Partial operator $\theta(y\mathbf{D}_{\lambda})$, based on the $\lambda$-derivative operator $\mathbf{D}_{\lambda}$, and use it to define the following generalization of the Lambert series…

This article presents the inverse of the kernel operator associated with the complete quadratic Lyapunov-Krasovskii functional for coupled differential-functional equations when the kernel operator is separable. Similar to the case of…

The purpose of this article is to study pseudospectral properties of the one-dimensional Schr\"{o}dinger operator perturbed by a complex steplike potential. By constructing the resolvent kernel, we show that the pseudospectrum of this…

We introduce a new integral transform $T^\lam f$, $\lam \in C^m$, on the Stiefel manifold of orthonormal $m$-frames in $R^n$ which generalizes the $\lam$-cosine transform on the Grassmann manifold of $m$-dimensional linear subspaces of…

We study a generalized Chebyshev oscillator [1] associated with a point interaction for the discrete Schr\"odinger equation. Our goal is to find a realization of the annihilation operator for this oscillator by a differential operator. This…

Multiparameter maximal estimates are considered for operators of Schr\"odinger type. Sharp and almost sharp results, that extend work by Rogers and Villarroya, are obtained. We provide new estimates via the integrability of the kernel which…

For time-periodical quantum systems generalized Floquet operator is found to be integral of motion.Spectrum of this invariant is shown to be quasienergy spectrum.Analogs of invariant Floquet operators are found for nonperiodical systems…