相关论文: Bispectrality of $N$-Component KP Wave Functions: …

We consider a polyharmonic operator $H=(-\Delta)^l+V(x)$ in dimension two with $l\geq 6$ and a limit-periodic potential $V(x)$. We prove that the spectrum of $H$ contains a semiaxis and there is a family of generalized eigenfunctions at…

We have recently constructed a photon position operator with commuting components. This was long thought to be impossible, but our position eigenvectors have a vortex structure like twisted light. Thus they are not spherically symmetric and…

Spectral operators of matrices proposed recently in [C. Ding, D.F. Sun, J. Sun, and K.C. Toh, Math. Program. {\bf 168}, 509--531 (2018)] are a class of matrix valued functions, which map matrices to matrices by applying a vector-to-vector…

We construct a commutative algebra A_z, generated by d algebraically independent q-difference operators acting on variables z_1, z_2,..., z_d, which is diagonalized by the multivariable Askey-Wilson polynomials P_n(z) considered by Gasper…

We study the distribution of eigenvalues for selfadjoint $h$--pseudodifferential operators in dimension two, arising as perturbations of selfadjoint operators with a periodic classical flow. When the strength $\varepsilon$ of the…

We show that the sectional curvature of a Riemannian manifold is nonnegative if, and only if, the entropy functional is matrix displacement convex. As an application we obtain intrinsic dimensional evolution variational inequalities, and…

In this paper we solve the following problems: (i) find two differential operators P and Q satisfying [P,Q]=P, where P flows according to the KP hierarchy \partial P/\partial t_n = [(P^{n/p})_+,P], with p := \ord P\ge 2; (ii) find a matrix…

Effects of noncommutativity are investigated in planar quantum mechanics in the coordinate representation. Generally these issues are addressed by converting to the momentum space. In the first part of the work we show noncommutative…

Using the bilinear formalism, we consider multicomponent and matrix modified KP hierarchies. The main tool is the bilinear identity for the tau-function which is realized as an expectation value of a Clifford group element composed from…

We show that for a winding number zero satellite operator $P$ on the knot concordance group, if the axis of $P$ has nontrivial self-pairing under the Blanchfield form of the pattern, then the image of the iteration $P^n$ generates an…

The eigenfunctions and eigenvalues of the Fokker-Planck operator with linear drift and constant diffusion are required for expanding time-dependent solutions and for evaluating our recent perturbation expansion for probability densities…

This paper is devoted to the definition and analysis of the spectral shift function (SSF) associated with non-self-adjoint perturbations of self-adjoint operators. Motivated by applications in scattering theory, we consider both trace-class…

A class of non-linear eigenvalue problems defined in the form of operator polynomials is investigated. The problems are related to wave equations which appear in a relativistic quantum field theory. Spectral asymptotics for this class are…

We study $I=3/2$ elastic $K\pi $ scattering to Born order using nonrelativistic quark wavefunctions in a constituent-exchange model. This channel is ideal for the study of nonresonant meson-meson scattering amplitudes since s-channel…

In this paper, we establish a condition on the coefficients of differential operators generated in the space of square-integrable functions on the entire real line by an ordinary differential expression with periodic, complex-valued…

Let $H_0$ and $H$ be self-adjoint operators in a Hilbert space. In the scattering theory framework, we describe the essential spectrum of the difference $\varphi(H)-\varphi(H_0)$ for piecewise continuous functions $\varphi$. This…

This is a summary of a recursive construction of solutions of the hbar-dependent KP hierarchy. We give recursion relations for the coefficients X_n of an hbar-expansion of the operator X = X_0 + \hbar X_1 + \hbar^2 X_2 + ... for which the…

We define functions of noncommuting self-adjoint operators with the help of double operator integrals. We are studying the problem to find conditions on a function $f$ on ${\Bbb R}^2$, for which the map $(A,B)\mapsto f(A,B)$ is Lipschitz in…

In this paper, we construct the additional flows of the noncommutative Kadomtsev-Petviashvili(KP) hierarchy and the additional symmetry flows constitute an infinite dimensional Lie algebra $W_{1+\infty}$. In addition, the generating…

It is known that, if a locally perturbed periodic self-adjoint operator on a combinatorial or quantum graph admits an eigenvalue embedded in the continuous spectrum, then the associated eigenfunction is compactly supported--that is, if the…