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Eigenvalue asymptotics and unique continuation of eigenfunctions on planar graphs
Annales De L'Institut FourierWe study planar graphs with large negative curvature outside of a finite set and the spectral theory of Schrödinger operators on these graphs. We obtain estimates on the first and second order term of the eigenvalue asymptotics. Moreover, we prove a unique continuation result for eigenfunctions and decay properties of general eigenfunctions. The proofs
Sylvain Golénia, Michel Bonnefont
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The calculation of eigenvalues and eigenfunctions in an asymptotically Coulomb potential
Computer Physics Communications, 1976Abstract The calculation of eigenvalues in a central field involves the matching, by Newton-Raphson or otherwise, of forward and backward trial solutions of the radial Schrodinger equation; the backward integration is commenced in a region where the potential has assumed its asymptotic form.
I.H. Aldeen, A.C. Allison, M.J. Jamieson
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Differential Equations, 2002
Het, the authors extend two results on the boundary problem \[ z(x)=x-\int_{0}^{l}{\nu(x-t)z(t)}\,d(\sigma(t)+t\lambda), \quad x\in{[0,l]}, \quad z(l)=0, \] obtained by them in two previous papers [\textit{V. A.Vinokurov}, Dokl. Math., 57, No. 1, 43--46 (1998; Zbl 0989.34016) and Dokl. Math., 59, No. 2, 220--222 (1999; Zbl 0967.34076)]. In these papers,
Vinokurov, V. A., Sadovnichii, V. A.
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Het, the authors extend two results on the boundary problem \[ z(x)=x-\int_{0}^{l}{\nu(x-t)z(t)}\,d(\sigma(t)+t\lambda), \quad x\in{[0,l]}, \quad z(l)=0, \] obtained by them in two previous papers [\textit{V. A.Vinokurov}, Dokl. Math., 57, No. 1, 43--46 (1998; Zbl 0989.34016) and Dokl. Math., 59, No. 2, 220--222 (1999; Zbl 0967.34076)]. In these papers,
Vinokurov, V. A., Sadovnichii, V. A.
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Asymptotic Behavior of Stekloff Eigenvalues and Eigenfunctions
SIAM Journal on Applied Mathematics, 1971We consider solutions $u_n (x,y)$ of Laplace’s equation which are regular in the interior of a smooth closed plane curve c, and the boundary conditions $\partial u_n /\partial v = \lambda _n gu_n $, where g is sufficiently smooth, positive, periodic and a prescribed function of arclength, and $u_n $, $\lambda _n $ are eigenfunctions and eigenvalues to ...
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Differential Equations, 2003
The authors consider the quasidifferential expression \[ L_{mn}(y) = \sum^{n}_{i=0}\sum^{m}_{j=0} (a_{ij}y^{(n-i)})^{(m-j)}, \quad m,n>0, \] on a finite interval \([a,b]\), where \(a_{00}\) is constant, \(a_{10}, a_{01} \equiv 0\), \(a_{i0}, a_{0j} \in L^{2}[a,b]\) and \(a_{ij}\) are derivatives of right continuous functions of bounded variation for ...
Makhnej, A. V., Tatsij, R. M.
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The authors consider the quasidifferential expression \[ L_{mn}(y) = \sum^{n}_{i=0}\sum^{m}_{j=0} (a_{ij}y^{(n-i)})^{(m-j)}, \quad m,n>0, \] on a finite interval \([a,b]\), where \(a_{00}\) is constant, \(a_{10}, a_{01} \equiv 0\), \(a_{i0}, a_{0j} \in L^{2}[a,b]\) and \(a_{ij}\) are derivatives of right continuous functions of bounded variation for ...
Makhnej, A. V., Tatsij, R. M.
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Asymptotic eigenfunctions and eigenvalues of a homogeneous integral equation
IEEE Transactions on Information Theory, 1962Summary: The eigenfunctions and eigenvalues of a certain integral equation are of importance in the Karhunen-Loève expansion of second-order stationary random functions. In this note the asymptotic eigenfunctions and eigenvalues of this integral equation are derived for the case where the kernel is the Fourier transform of a rational function of ...
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Refined asymptotic formulas for eigenvalues and eigenfunctions of the Dirac system
Doklady Mathematics, 2012The authors study the Dirac system \[ \begin{aligned} &y'_1 (x) - q_2 (x)y_2 (x) = \lambda y_1 (x), \\ &y'_2 (x) - q_1 (x)y_1 (x) = - \lambda y_2 (x)\end{aligned} \] with boundary conditions \[ y_1 (0) = y_2 (0),\,\,\,\,\,y_1 (1) = y_2 (1). \] Using a method based on transformation operator formulas, refined asymptotic formulas for the nonsmooth case ...
Burlutskaya, M. Sh. +2 more
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Asymptotic formulae for eigenvalues and eigenfunctions of \(q\)-Sturm-Liouville problems
2011Wiley Online ...
Annaby, Mahmoud H., Mansour, Zeinab S.
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On the Asymptotic Behavior of Eigenvalues and Eigenfunctions of Non-Self-Adjoint Elliptic Operators
Journal of Mathematical Sciences, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pyatnitskiĭ, A. L., Shamaev, A. S.
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Journal of the London Mathematical Society, 1999
An asymptotically perturbed cylinder is a manifold which, to the exterior of a compact set, is of the form \(\mathbb{R}\times M\), where \(M\) is a compact manifold (with or without boundary), and for which the metric approaches the product metric as the axial variable tends to infinity.
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An asymptotically perturbed cylinder is a manifold which, to the exterior of a compact set, is of the form \(\mathbb{R}\times M\), where \(M\) is a compact manifold (with or without boundary), and for which the metric approaches the product metric as the axial variable tends to infinity.
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