Related papers: Stability in Non-Normal Periodic Jacobi Operators:…
A theory for stabilization of quantum resonances by a mechanism similar to one leading to classical resonances in nonlinear systems is presented. It explains recent surprising experimental results, obtained for cold Cesium atoms when driven…
A family $\BA_\a$ of differential operators depending on a real parameter $\a$ is considered. The problem can be formulated in the language of perturbation theory of quadratic forms. The perturbation is only relatively bounded but not…
We develop a theory of regularity for Dirac operators with uniformly locally square-integrable operator data. This is motivated by Stahl--Totik regularity for orthogonal polynomials and by recent developments for continuum Schr\"odinger…
We consider the effects of varying dispersion and nonlinearity on the stability of periodic traveling wave solutions of nonlinear PDE of KdV-type, including generalized KdV and Benjamin-Ono equations. In this investigation, we consider the…
The paper studies the global convergence of the block Jacobi me\-thod for symmetric matrices. Given a symmetric matrix $A$ of order $n$, the method generates a sequence of matrices by the rule $A^{(k+1)}=U_k^TA^{(k)}U_k$, $k\geq0$, where…
The spectral behavior of the difference between the resolvents of two realizations $\tilde A_1$ and $\tilde A_2$ of a second-order strongly elliptic symmetric differential operator $A$, defined by different Robin conditions $\nu…
Jacobi is one of the most famous mathematicians of his century. His name is attached to many results in various fields of mathematics and his complete works in seven volumes have been available since the end of the XIXth century and are…
We study the bispectrality of Jacobi type polynomials, which are eigenfunctions of higher-order differential operators and can be defined by taking suitable linear combinations of a fixed number of consecutive Jacobi polynomials. Jacobi…
The Jacobi matrices with bounded elements whose spectrum of multiplicity 2 is separated from its simple spectrum and contains an interval of absolutely continuous spectrum are considered. A new type of spectral data, which are analogous for…
We study the spectral theory of a class of piecewise centrosymmetric Jacobi operators defined on an associated family of substitution graphs. Given a finite centrosymmetric matrix viewed as a weight matrix on a finite directed path graph…
This paper investigates the stability properties of neural operators through the structured representation offered by the Hybrid B-spline Deep Neural Operator (HBDNO). While existing stability-aware architectures typically enforce…
Perturbations of a class of semiclassical strings known today as spiky strings, are studied using the well-known Jacobi equations for small normal deformations of an embedded timelike surface. It is shown that there exists finite normal…
We consider the 1D periodic Jacobi matrices. The spectrum of this operator is purely absolutely continuous and consists of intervals separated by gaps. We solve the inverse problem (including characterization) in terms of vertical slits on…
The real Ginzburg-Landau equation arises as a universal amplitude equation for the description of pattern-forming systems exhibiting a Turing bifurcation. It possesses spatially periodic roll solutions which are known to be stable against…
This paper deals with general structural properties of one-dimensional Schr"odinger operators with some absolutely continuous spectrum. The basic result says that the omega limit points of the potential under the shift map are…
This paper explains the fundamental relation between Jacobi structures and the classical Spencer operator coming from the theory of PDEs so as to provide a direct and geometric approach to the integrability of Jacobi structures. It uses…
In this paper, we introduce the B-discrete spectrum of an unbounded closed operator and we prove that a closed operator has a purely B-discrete spectrum if and only if it has a meromorphic resolvent. After that, we study the stability of…
We present in this work a proof of the exponential dichotomy for dynamically defined matrix-valued Jacobi operators in $(\mathbb{C}^{l})^{\mathbb{Z}}$, given for each $\omega \in \Omega$ by the law $[H_{\omega} \textbf{u}]_{n} := D(T^{n -…
The number and relative placement of BPMs and steerers with respect to the quadrupoles in a circular lattice can lead to degeneracy in the context of inverse modeling of accelerator optics. Further, the measurement uncertainties introduced…
We consider periodic Jacobi operators and obtain upper and lower estimates on the sizes of the spectral bands. Our proofs are based on estimates on the logarithmic capacities and connections between the Chebyshev polynomials and logarithmic…