Related papers: Inverse problems for Jacobi operators with finitel…
Under consideration are mathematical models of heat and mass transfer. We study inverse problems of recovering lower-order coefficients in a second order parabolic equation. The coefficients are representable in the form of a finite…
The variation of spectral subspaces for linear self-adjoint operators under an additive bounded perturbation is considered. The objective is to estimate the norm of the difference of two spectral projections associated with isolated parts…
We introduce a class of Jacobi operators with discrete spectra which is characterized by a simple convergence condition. With any operator J from this class we associate a characteristic function as an analytic function on a suitable…
In this paper we study spectral properties of Jacobi operators. In particular, we prove two main results: (1) that perturbing the diagonal coefficients of Jacobi operator, in an appropriate sense, results in exponential localization, and…
We construct noncomplete orthogonal systems on the ray $[0,\infty)$ that look like Jacobi polynomials $P_n(x)$ after a shift of degree $n\mapsto n+a$, where $a$ is a real constant. These systems are solutions of some exotic Sturm-Liouville…
We obtain a finite form of Jacobi's identity and present a combinatorial proof based on the structure of synchronized partitions.
We present a general framework to study uniqueness, stability and reconstruction for infinite-dimensional inverse problems when only a finite-dimensional approximation of the measurements is available. For a large class of inverse problems…
Some properties and relations satisfied by the polynomial solutions of the bispectral problem are studied. Given a differential operator, under certain restrictions its polynomial eigenfunctions are explicitly obtained, as well as the…
The spectral properties of a class of band matrices are investigated. The reconstruction of matrices of this special class from given spectral data is also studied. Necessary and sufficient conditions for that reconstruction are found. The…
In this paper we study Jacobi forms associated with the Leech lattice $\Lambda$ which are invariant under the Conway group $\mathrm{Co}_0$. We determine and construct generators of modules of both weak and holomorphic Jacobi forms of…
We consider matrices on infinite trees which are universal covers of Jacobi matrices on finite graphs. We are interested in the question of the existence of sequences of finite covers whose normalized eigenvalue counting measures converge…
In this paper we approximate a Schr\"odinger operator on $L^2(\R)$ by Jacobi operators on $\ell^2(\Z)$ to provide new proofs of sharp Lieb-Thirring inequalities for the powers $\gamma=1/2$ and $\gamma=3/2$. To this end we first investigate…
The 2-dimensional inverse problem for first-order systems is analysed and a method to construct an affine Lagrangian for such systems is developed. The determination of such Lagrangians is based on the theory of the Jacobi multiplier for…
We consider matrix orthogonal polynomials related to Jacobi type matrices of weights that can be defined in terms of a given matrix Pearson equation. Stating a Riemann-Hilbert problem we can derive first and second order differential…
We introduce an operator on problems in Weihrauch complexity, which we call the inverse limit, and which corresponds to an infinite compositional product. This operation arises naturally whenever one implements algorithms that produce a…
In this work the spectral theory of self-adjoint operator $A$ represented by Jacobi matrix is considered. The approach is based on the continued fraction representation of the resolvent matrix element of $A$. Different criteria of absolute…
Operadic Lax representations for the harmonic oscillator are used to construct the quantum counterparts of three-dimensional real Lie algebras. The Jacobi operators of these quantum algebras are explicitly calculated.
In this paper we solve an inverse resonance problem for the half-solid with vanishing stresses on the surface: Lamb's problem. Using a semi-classical approach we are able to simplify this three-dimensional problem of the elastic wave…
The Jacobian conjecture over a field of characteristic zero is considered directly in view of the nonlinear partial differential equations it is associated with. Exploring the integrals of such partial differential equations, this work…
This paper concerns some inverse eigenvalue problems of the quadratic $\star$-(anti)-palindromic system $Q(\lambda)=\lambda^2 A_1^{\star}+\lambda A_0 + \epsilon A_1$, where $\epsilon=\pm 1$, $A_1, A_0 \in \mathbb{C}^{n\times n}$,…