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have problem in understanding the fourier series and eigenfunction expansion

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#fourier-series #eigenfunctions
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confused about why this coefficient of fourier series is defined as so

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#fourier-series #eigenfunctions
900
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Consider the Sturm-Liouville problem $y^{\prime\prime}+ \lambda y=0,y(0)=y( \pi)=0.$

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#ordinary-differential-equations #eigenvalues-eigenvectors #boundary-value-problem #eigenfunctions #sturm-liouville
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What does it mean by family of a function is complete?

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#partial-differential-equations #fourier-series #eigenfunctions
79
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Does this BVP have an analytic solution?

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#ordinary-differential-equations #asymptotics #boundary-value-problem #eigenfunctions
81
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Finding eigenfunction(s)

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#ordinary-differential-equations #boundary-value-problem #eigenfunctions
63
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Reference Request:Real analyticity of smooth eigenforms of the Laplacian

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#differential-geometry #riemannian-geometry #eigenfunctions #regularity-theory-of-pdes #hodge-theory
58
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Estimation of low bounde of gradient of eigenfunction on circle .

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#partial-differential-equations #eigenfunctions
57
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eigen functions of finite filters

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#fourier-analysis #fourier-transform #convolution #signal-processing #eigenfunctions
48
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Eigenvalues and eigenspaces of differential operator on finitely generated vector space

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#linear-algebra #eigenvalues-eigenvectors #eigenfunctions #differential-operators
317
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How to verify the following function is an eigen-function of the given operator

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#bessel-functions #eigenfunctions #differential-operators
201
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Why do solutions tend to move towards the eigen-span in a differential equation?

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#linear-algebra #ordinary-differential-equations #eigenvalues-eigenvectors #linear-transformations #eigenfunctions
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Facts About Eigenvectors and Eigenvalues

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#linear-algebra #eigenvalues-eigenvectors #eigenfunctions
110
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A contradiction? Inconsistent expression of Hermite functions as eigenvalues of Fourier transform.

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#fourier-analysis #eigenfunctions #hermite-polynomials
228
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Umbral calculus - eigenfunctions of operator

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#calculus #operator-theory #eigenfunctions #umbral-calculus

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