eigenfunction

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eigenfunction

(ˈaɪɡənˌfʌŋkʃən)
n
(Mathematics) maths physics a function satisfying a differential equation, esp an allowed function for a system in wave mechanics
Translations
Eigenfunktion
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This can be recast in terms of fourier analysis on the hypercube: A function is noise sensitive iff most of its fourier weight is on "high energy" eigenfunctions of the random walk operator.
Eigenfunctions of the Laplacian of a Riemannian Manifold
1) "though the form in which the degeneration of the free electron is now treated in the paper would seem to be unambiguous" (2) "The difficulty was the eigenfunction in the presence of a magnetic field, a point which I think is not completely cleared up yet" (3) "Therefore the eigenfunctions you have used in your paper are not so simply as we thought connected with the "spin" " (4) "but this has no influence on your results, only the sentences where spin comes in could not have quite the definite form you gave them" The second letter,(11,23) dated 2nd Dec.
Sarnak, Quantum ergodicity of eigenfunctions on [PSL.
Commonly, PSWFs are known as the eigenfunctions of Sturm-Liouville differential operator [4]:
Since the deformation is expressed as eigenfunctions products, the solution of the dynamic problem is obtained based on the orthogonality properties of eigenfunctions.
MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are all eigenfunctions of operator [L.
possess the same system of eigenfunctions, with that, we regard [?
In this way, we consider the piecewise construction of eigenfunctions for all possible discrete k [member of] C that make sense of the following system:
Solutions to (1) completely characterize membrane motions since the eigenfunctions form a complete orthonormal basis for the space of membrane vibrations.
In [24], Tuna and Eryilmaz proved a theorem on completeness of the system of eigenfunctions and associated functions of dissipative q-Sturm-Liouville operators by using the Lidskii's theorem.
The inverse nodal problem lies in the use of nodal points of the eigenfunctions of (1)-(3) as spectral parameters.