Let M be a space of weakly*-measurable functions F : ? B(H) on measure (?,?,?), for which the function F*F is Gel'fand integrable and integral d? nuclear operator Hilbert H. We show that H*-module contains an orthonormal basis.

In this article we consider two particular examples of general construction proposed in arXiv:2012.15529. We the integrable extensions classical elliptic Calogero-Moser model N particles with spin and Euler-Arnold top related to group SL(N,C). The extended systems has additional N-1 degrees freedom can be described terms Darboux variables.

Abstract The partition function of the Symmetric Matrix Ensemble is identified with $$\tau $$ ? -function a particular solution Pfaff Lattice. We show that, in case even power interactions, thermodynamic limit, corresponds to an integrable chain hydrodynamic type. prove that so obtained diagonalisable and adm...

Let $\mathcal{M}$ be the bilinear Hardy-Littlewood maximal function and $\vec{b}=(b,b)$ a collection of locally integrable functions. In this paper, authors establish characterizations weighted {\rm BMO} space in terms several different commutators function, respectively; these include iterated commutator $\mathcal{M}_{\Pi \vec{b}}$, linear $\mathcal{M}_{\Sigma\vec{b}}$, $[\Pi \vec{b},\mathcal{...

we regard the shearlet group as a semidirect product group andshow that its standard representation is,typically, a quasiregu-lar representation. as a result we can characterize irreducibleas well as square-integrable subrepresentations of the shearletgroup.

Assuming preferences to be generated by an aggregate utility function, an aggregate demand function for imports and exports is defined as a function of import and export prices and the deficit in the balance of payments on current account, in a model with nontradable as well as traded goods. It is shown that this function is integrable, hence can be generated by maximizing a utility function (w...

Based on a kind of special non-semisimple Lie algebras, a scheme is presented for constructing nonlinear continuous integrable couplings. Variational identities over the corresponding loop algebras are used to furnish Hamiltonian structures for the resulting continuous integrable couplings. The application of the scheme is illustrated by an example of nonlinear continuous integrable Hamiltonian...

The Szekeres model is a differential system in R4 that provides the solutions of Einstein field equations presence irrotational dust. This integrable with two rational first integrals and one analytic integral. We characterize qualitative behavior all orbits function values integrals.

This paper connects the analysis of the length of the longest weakly increasing subsequence of inhomogeneous random words to a Riemnn-Hilbert problem and an associated system of integrable partial differential equations. In particular, we show that the Poissonization of the distribution function of this length can be identified as the Jimbo-Miwa-Ueno tau function. © 2001 Elsevier Science B.V. A...

Let M be a noncompact complete Riemannian manifold. We consider the Schrödinger operator −∆ + V acting on L2(M), where V is a nonnegative, locally integrable function on M . We obtain some simple conditions which imply that inf Spec(−∆ + V ), the bottom of the spectrum of −∆ + V , is strictly positive. We also establish upper and lower bounds for the counting function N(λ).