Results 191 to 200 of about 15,892 (238)
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On special orthogonal eigenfunctions and eigenfunction expansions
International Journal of Mathematical Education in Science and Technology, 1996We extend some earlier results while illustrating solution techniques commonly encountered by students in undergraduate and beginning graduate courses of mathematical analysis, differential equations, and engineering mathematics. Previously, Turan's inequality was established by using a technique known as the Prufer substitution.
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Atomic Eigenfunctions and Energies
Physical Review, 1932In \textsection{}1, the calculation of the nondiagonal elements of electrostatic interaction is sketched. In \textsection{}2, attention is called to the fact that the matrix elements of ${L}_{x}$ (the $x$-component of orbital angular momentum), as calculated between spherical harmonic eigenfunctions taken with positive phase, are negative when ${m}_{l}$
Ufford, C. W., Shortley, G. H.
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The Eigenfunctions of the Hilbert Matrix
Constructive Approximation, 2012The authors consider the Hilbert matrix \(H_{\lambda}=(\frac{1}{n+m+\lambda})_{n, m\geq 0}\), where \(\lambda \in {\mathbb C}\), \(\lambda \notin {\mathbb Z}\). Let \(X\) be one of the Banach spaces \(H^p, A^{-\tau }, A^{-\tau }_0\) of analytical functions on the unit disc of \(\mathbb C\).
Aleman, Alexandru +2 more
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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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On the Smallness of Isolated Eigenfunctions
American Journal of Mathematics, 1949which is satisfied by x yj(t) at t = 0). According to Weyl [3], p. 238, the assumption (2) precludes the existence of a A0 corresponding to which (3) had two linearly independent solutions of class (L2). Correspondingly, every boundary condition (5) determines for (1) a spectrum S(p), containing a (possibly vacuous) point spectrum P(p).
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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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