Geodesic
Left-definite variations of the classical Fourier expansion theorem
Electronic transactions on numerical analysis, Tome 27 (2007), pp. 124-139
In a recent paper, Littlejohn and Wellman developed a general left-definite theory for arbitrary selfadjoint operators in a Hilbert space that are bounded below by a positive constant. We apply this theory and construct the sequences of left-definite Hilbert spaces and left-definite self-adjoint operators associated $\sterling $########

${\S}$

###$\copyright \ddot \sterling $###$\ddot $### ###

$ with the classical, regular self-adjoint boundary value problem consisting of the Fourier equation with periodic boundary conditions. As a particular consequence of our analysis, we obtain a Fourier expansion theorem in each left-definite space as well as an explicit representation of the domain of $

###$"!# for each positive integer .$
Classification : 34B24, 33B10
Keywords: self-adjoint operator, Hilbert space, left-definite Hilbert space, left-definite operator, regular selfadjoint boundary value problem, Fourier series 
@article{ETNA_2007__27__a3,
     author = {Littlejohn,  L.L. and Zettl,  A.},
     title = {Left-definite variations of the classical {Fourier} expansion theorem},
     journal = {Electronic transactions on numerical analysis},
     pages = {124--139},
     year = {2007},
     volume = {27},
     zbl = {1181.47050},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2007__27__a3/}
}
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%A Zettl,  A.
%T Left-definite variations of the classical Fourier expansion theorem
%J Electronic transactions on numerical analysis
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%F ETNA_2007__27__a3
Littlejohn,  L.L.; Zettl,  A. Left-definite variations of the classical Fourier expansion theorem. Electronic transactions on numerical analysis, Tome 27 (2007), pp. 124-139. http://geodesic.mathdoc.fr/item/ETNA_2007__27__a3/