On the $$R$$-matrix identities related to elliptic anisotropic spin Ruijsenaars–Macdonald operators
نویسندگان
چکیده
We propose and prove a set of identities for ${\rm GL}_M$ elliptic $R$-matrix (in the fundamental representation). In scalar case ($M=1$) these are function derived by S.N.M. Ruijsenaars as necessary sufficient conditions his kernel identity underlying construction integral solutions to quantum spinless Ruijsenaars-Schneider model. this respect result present paper can be considered first step towards constructing eigenvalue problem anisotropic spin
منابع مشابه
The spectral properties of differential operators with matrix coefficients on elliptic systems with boundary conditions
Let $$(Lv)(t)=sum^{n} _{i,j=1} (-1)^{j} d_{j} left( s^{2alpha}(t) b_{ij}(t) mu(t) d_{i}v(t)right),$$ be a non-selfadjoint differential operator on the Hilbert space $L_{2}(Omega)$ with Dirichlet-type boundary conditions. In continuing of papers [10-12], let the conditions made on the operator $ L$ be sufficiently more general than [11] and [12] as defined in Section $1$. In this paper, we estim...
متن کاملPohozaev Identities for Anisotropic Integro-differential Operators
We establish Pohozaev identities and integration by parts type formulas for anisotropic integro-differential operators of order 2s, with s ∈ (0, 1). These identities involve local boundary terms, in which the quantity u/d|∂Ω plays the role that ∂u/∂ν plays in the second order case. Here, u is any solution to Lu = f(x, u) in Ω, with u = 0 in R \ Ω, and d is the distance to ∂Ω.
متن کاملON COMPACT OPERATORS ON SOME SPACES RELATED TO MATRIX B ( r , s )
Many sequence spaces arise from different concepts of summability. Recent results obtained by Altay, Başar and Malkowsky [2] are related to strong Cesàro summability and boundedness. They determined β−duals of the new sequence spaces and characterized some classes of matrix transformations on them. Here, we will present new results supplementing their research with the characterization of class...
متن کاملLaplace operators related to self - similar measures on R d
Given a bounded open subset Ω of Rd (d 1) and a positive finite Borel measure μ supported on Ω with μ(Ω) > 0, we study a Laplace-type operator μ that extends the classical Laplacian. We show that the properties of this operator depend on the multifractal structure of the measure, especially on its lower L∞-dimension dim∞(μ). We give a sufficient condition for which the Sobolev space H 1 0 (Ω) i...
متن کاملExistence of ℋ-matrix approximants to the inverse FE-matrix of elliptic operators with L∞-coefficients
This article deals with the existence of blockwise low-rank approximants — so-called H-matrices — to inverses of FEM matrices in the case of uniformly elliptic operators with L∞-coefficients. Unlike operators arising from boundary element methods for which the H-matrix theory has been extensively developed, the inverses of these operators do not benefit from the smoothness of the kernel functio...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Theoretical and Mathematical Physics
سال: 2022
ISSN: ['1864-5887', '1864-5879']
DOI: https://doi.org/10.1134/s0040577922110046