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

The Baker-Akhiezer (wave) functions corresponding to soliton solutions of the KP hierarchy are shown to satisfy eigenvalue equations for a commutative ring of translational operators in the spectral parameter. In the rational limit, these…

It is by now well known that the wave functions of rational solutions to the KP hierarchy (those which can be achieved as limits of the pure n-soliton solutions) satisfy an additional eigenvalue equation for ordinary differential operators…

Pairs of $n\times n$ matrices whose commutator differ from the identity by a matrix of rank $r$ are used to construct bispectral differential operators with $r\times r$ matrix coefficients satisfying the Lax equations of the Matrix KP…

Starting from free charged fermions we give equivalent definitions of the $n\/$-component KP hierarchy, in terms of $\tau\/$-functions $\tau_\alpha\/$ (where $\alpha \in M =\/$ root lattice of $sl_n\/$), in terms of $n \times n\/$ matrix…

It is by now well known that the wave functions of rational solutions to the KP hierarchy which can be achieved as limits of the pure $n$-soliton solutions satisfy an eigenvalue equation for ordinary differential operators in the spectral…

I revisit the so called "bispectral problem" introduced in a joint paper with Hans Duistermaat a long time ago, allowing now for the differential operators to have matrix coefficients and for the eigenfunctions, and one of the eigenvalues,…

The subject of time-band-limiting, originating in signal processing, is dominated by the miracle that a naturally appearing integral operator admits a commuting differential one allowing for a numerically efficient way to compute its…

We consider the analytic continuation of the transfer function for a 2x2 matrix Hamiltonian into the unphysical sheets of the energy Riemann surface. We construct a family of non-selfadjoint operators which reproduce certain parts of the…

Questions on random matrices and on non-intersecting Brownian motions have led to the study of moment matrices with regard to several weights. The purpose of this paper is to show that the determinants of such moment matrices satisfy, upon…

The Kramers-Wannier self-duality of critical quantum chains is examined from the perspective of model wave functions. We demonstrate, using the transverse-field Ising chain and the $3$-state Potts chain as examples, that the symmetry…

We consider the analytic continuation of the transfer function for a 2x2 matrix Hamiltonian into the unphysical sheets of the energy Riemann surface. We construct non-selfadjoint operators representing operator roots of the transfer…

We consider operator matrices {\bf H}= (A_0 B_{01} \\ B_{10} A_{1}) with self-adjoint entries A_i, i=0,1, and bounded B_{01}=B_{10}^*, acting in the orthogonal sum {\cal H}={\cal H}_0\oplus{\cal H}_1 of Hilbert spaces {\cal H}_0 and {\cal…

Let G/K be an irreducible Hermitian symmetric space and let D be a K-invariant domain in G/K. In this paper we characterize several classes of K-invariant plurisubharmonic functions on D in terms of their restrictions to a slice…

In this article, we show that four sets of differential Fay identities of an $N$-component KP hierarchy derived from the bilinear relation satisfied by the tau function of the hierarchy are sufficient to derive the auxiliary linear…

We study various properties of a nonperturbative partition function which can be associated to any spectral curve. When the spectral curve arises from a matrix model, this nonperturbative partition function is given by a sum of matrix…

Bispectral analysis of the nonlinear resonant interaction known as parametric subharmonic instability (PSI) for a coherence semidiurnal internal tide demonstrates the ability of the bispectrum to identify and quantify the transfer rate.…

Finite rank perturbations $T=N+K$ of a bounded normal operator $N$ on a separable Hilbert space are studied thanks to a natural functional model of $T$; in its turn the functional model solely relies on a perturbation matrix/ characteristic…

In this paper, we investigate the eigenvalue problem for a non-local dispersal operator defined on a bounded spatial domain with Neumann-type boundary conditions. Unlike the classical Laplacian, the non-local operator lacks compactness,…

We provide a complete description of the spectrum and the essential spectra of weighted composition operators $T=wT_\varphi$ on $C(K)$ in the case when the map $\varphi$ is a non-invertible homeomorphism of $K$ into itself.

The time periodic circuit theory is exploited to introduce an appropriate translation operator that is invariant under the change of the spatial unit cell. Useful properties of the operator are derived. By casting the problem in an…