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pro vyhledávání: '"34B24"'
The purpose of this paper is to study nonnegative self-adjoint extensions associated with singular Sturm-Liouville expressions with strictly positive minimal operators. We provide a full characterization of all possible nonnegative self-adjoint exten
Externí odkaz:
http://arxiv.org/abs/2410.04647
Autor:
Rummler, Bernd, Thäter, Gudrun
We consider the Stokes eigenvalue problem in open balls and open annuli in R3 with homogeneous Dirichlet boundary conditions. Using the frame of toroidal and poloidal fields we construct the othogonal decomposition of the Stokes eigenvalue problem in
Externí odkaz:
http://arxiv.org/abs/2408.06948
Let v_1 and v_2 be two distinct vertices of a tree T_0. Let \phi_N^{(i)} (i=1,2) be the characteristic functions of the Sturm-Liouville problem on T_0 rooted at v_i with Neumann conditions at the root and let \phi_D^{(i)} (i=1,2) be the characteristi
Externí odkaz:
http://arxiv.org/abs/2408.01995
Autor:
Gesztesy, Fritz, Pang, Michael M. H.
We derive an optimal power-weighted Hardy-type inequality in integral form on finite intervals and subsequently prove the analogous inequality in differential form. We note that the optimal constant of the latter inequality differs from the former. M
Externí odkaz:
http://arxiv.org/abs/2408.01884
In the present paper, motivated by point interaction, we propose a new and explicit approach to inverse Sturm-Liouville eigenvalue problems under Dirichlet boundary. More precisely, when a given Sturm-Liouville eigenvalue problem with the unknown int
Externí odkaz:
http://arxiv.org/abs/2407.17223
In this paper we introduce an index $\ell_c \in \mathbb{N}_0 \cup \lbrace \infty \rbrace$ which we call the `regularization index' associated to the endpoints, $c\in\{a,b\}$, of nonoscillatory Sturm-Liouville differential expressions with trace class
Externí odkaz:
http://arxiv.org/abs/2407.04847
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:
Galo-Mendoza, Leandro
In this paper, we prove the null controllability of a one-dimensional fourth-order degenerate parabolic equation with a singular potential. Here, we analyze cases where boundary control conditions are applied at the left endpoint. We utilize a spectr
Externí odkaz:
http://arxiv.org/abs/2403.08745
Autor:
Connes, Alain
We compute the full asymptotic expansion of the heat kernel Trace$(\exp(-tD^2))$ where $D$ is, assuming RH, the self-adjoint operator whose spectrum is formed of the imaginary parts of non-trivial zeros of the Riemann zeta function. The coefficients
Externí odkaz:
http://arxiv.org/abs/2402.13082
Autor:
Karjanto, N., Sadhani, P.
The Sturm-Liouville boundary value problem (SLBVP) stands as a fundamental cornerstone in the realm of mathematical analysis and physical modeling. Also known as the Sturm-Liouville problem (SLP), this paper explores the intricacies of this classical
Externí odkaz:
http://arxiv.org/abs/2402.00408