Results 171 to 180 of about 20,411 (217)
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Some Properties of Eigenfunctions
SIAM Journal on Applied Mathematics, 1975The purpose of this paper is to find simple relations between properties of eigenfunctions $y( x )$ and the density function $p( x )$ of the system $y'' + \lambda p( x )y = 0,y( { \pm 1} ) = 0$.
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Factorization Ladders and Eigenfunctions
Canadian Journal of Mathematics, 1949The eigenfunctions of a boundary value problem are characterized by two quite distinct properties. They are solutions of ordinary differential equations, and they satisfy prescribed boundary conditions. It is a definite advantage to combine these two requirements into a single problem expressed by a unified formula.
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Riesz Bases of Eigenfunctions and Adjoint Eigenfunctions of Some Integral Operators
Differential Equations, 2002Consider the integral operator \[ A f(x) = \int_0^{1-x} ( 1+ A(1-x, t)) f(t) dt , \quad x \in [0, t], \tag{1} \] acting in \(L_2 [0, 1]\). The author shows that the root vectors of the operator \(A\) form a Riesz basis in \(L_2 [0, 1]\) under the assumptions that the function \(A(x, t)\) and its first order derivative with respect to \(x\) are ...
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Approach to energy eigenvalues and eigenfunctions from nonperturbative regions of eigenfunctions
Physical Review E, 2001We study the approach to energy eigenvalues and eigenfunctions of Hamiltonian matrices with band structure from diagonalization of their truncated matrices. Making use of a generalization of Brillouin-Wigner perturbation theory, it is shown that in order to obtain approximate energy eigenvalues and eigenfunctions the sizes of truncated matrices should ...
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Embedding of eigenfunctions of the Johnson graph into eigenfunctions of the Hamming graph
Journal of Applied and Industrial Mathematics, 2014Summary: The relationship between the eigenfunctions of Johnson and Hamming graphs is studied. An eigenfunction of a graph is an eigenvector of its adjacency matrix with some eigenvalue; moreover, an eigenfunction can be identically zero. We find a criterion for the embeddability of an eigenfunction of the Johnson graph \(J(n,w)\) with a given ...
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On Singularities in Eigenfunctions
The Journal of Chemical Physics, 1965The relationship between some singularities of the eigenfunction and convergence of the Legendre expansion is studied for the ground state of the helium atom.
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ON EXPANSIONS IN EIGENFUNCTIONS (VI)
The Quarterly Journal of Mathematics, 1940openaire +1 more source
On Expansions in Eigenfunctions
Journal of the London Mathematical Society, 1939openaire +2 more sources
Computation of Eigenvalues and Eigenfunctions in the Solution of Eddy Current Problems
Sensors, 2023Anastassios Skarlatos +2 more
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