Zobrazeno 1 - 10
of 431
pro vyhledávání: '"34L10"'
Autor:
Parisi, Ignacio Bono, Pacharoni, Inés
In the theory of matrix-valued orthogonal polynomials, there exists a longstanding problem known as the Matrix Bochner Problem: the classification of all $N \times N$ weight matrices $W(x)$ such that the associated orthogonal polynomials are eigenfun
Externí odkaz:
http://arxiv.org/abs/2411.00798
Autor:
Anguas, L. M., Rolanía, D. Barrios
A sequence $\{\delta_n^{(k)}\}$ associated to a Bochner differential operator is introduced as an effective tool to study this kind of operators. Some properties of this sequence are proven and used to deduce that a particular operator leads to solut
Externí odkaz:
http://arxiv.org/abs/2410.07449
Autor:
Mingarelli, Angelo B.
We prove an old conjecture that relates the existence of non-real eigenvalues of Sturm-Liouville Dirichlet problems on a finite interval to the non-existence of oscillation numbers of its real eigenfunctions, [[6], p.104, Problems 3 and 5]. This exte
Externí odkaz:
http://arxiv.org/abs/2404.19575
Autor:
Parisi, Ignacio Bono, Pacharoni, Inés
The Matrix Bochner Problem aims to classify weight matrices $W$ such that its algebra $\mathcal D(W)$, of all differential operators that have a sequence of these matrix orthogonal polynomials as eigenfunctions, contains a second-order differential o
Externí odkaz:
http://arxiv.org/abs/2403.03873
Autor:
Harutyunyan, Tigran, Ashrafyan, Yuri
The main issues of the spectral theory of Dirac operators are presented, namely: transformation operators, asymptotics of eigenvalues and eigenfunctions, description of symmetric and self-adjoint operators in Hilbert space, expansion in eigenfunction
Externí odkaz:
http://arxiv.org/abs/2403.02761
Autor:
Makin, Alexander
The paper is concerned with the completeness property of root functions of the $2\times 2$ Dirac operator with summable complex-valued potential and non-regular boundary conditions. Sufficient conditions for the completeness of the root function syst
Externí odkaz:
http://arxiv.org/abs/2401.02232
Autor:
Lunyov, Anton A., Malamud, Mark M.
The paper is concerned with the completeness property of the system of root vectors of a boundary value problem for the following $2 \times 2$ Dirac type equation $$ L y = -i B^{-1} y' + Q(x) y = \lambda y , \quad y= {\rm col}(y_1, y_2), \quad x \in
Externí odkaz:
http://arxiv.org/abs/2312.15933
Autor:
Zolotarev, Vladimir A.
Scattering problem for a self-adjoint integro-differential operator, which is the sum of the operator of second derivative and of a finite-dimensional self-adjoint operator, is studied. Jost solutions are found and it is shown that the scattering fun
Externí odkaz:
http://arxiv.org/abs/2312.14545
Autor:
Gesztesy, Fritz, Hunziker, Markus
We consider the generalized eigenvalue problem for the classical Euler differential equation and demonstrate its intimate connection with Meijer's $G$-functions. In the course of deriving the solution of the generalized Euler eigenvalue equation we r
Externí odkaz:
http://arxiv.org/abs/2311.13083
Autor:
Amiri, Manouchehr
Publikováno v:
International Journal of Pure and Applied Mathematics Research, 2023
The present paper introduces a method of basis transformation of a vector space that is specifically applicable to polynomials space and differential equations with certain polynomials solutions such as Hermite, Laguerre and Legendre polynomials. Thi
Externí odkaz:
http://arxiv.org/abs/2311.06058