Geodesic
Beurlings theorem for functions with essential spectrum from homogeneous spaces and stabilization of solutions of parabolic equations
Matematičeskie zametki, Tome 92 (2012) no. 5, pp. 643-661

Voir la notice de l'article provenant de la source Math-Net.Ru

The results of the paper are obtained for functions from homogeneous spaces of functions defined on a locally compact Abelian group. The notion of the Beurling spectrum, or essential spectrum, of functions is introduced. If a continuous unitary character is an essential point of the spectrum of a function, then it is the $\mathrm{c}$-limit of a linear combination of shifts of the function in question. The notion of a slowly varying function at infinity is introduced, and the properties of such functions are considered. For a parabolic equation with initial function from a homogeneous space, it is proved that the weak solution as a function of the first argument is a slowly varying function at infinity.
Keywords: Beurling spectrum of a function, locally compact Abelian group, continuous unitary character, Banach space, Banach module, directed set, Stepanov set.
Mots-clés : parabolic equation, Fourier transform 
@article{MZM_2012_92_5_a0,
     author = {A. G. Baskakov and N. S. Kaluzhina},
     title = {Beurlings theorem for functions with essential spectrum from homogeneous spaces and stabilization of solutions of parabolic equations},
     journal = {Matemati\v{c}eskie zametki},
     pages = {643--661},
     publisher = {mathdoc},
     volume = {92},
     number = {5},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_92_5_a0/}
}
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A. G. Baskakov; N. S. Kaluzhina. Beurlings theorem for functions with essential spectrum from homogeneous spaces and stabilization of solutions of parabolic equations. Matematičeskie zametki, Tome 92 (2012) no. 5, pp. 643-661. http://geodesic.mathdoc.fr/item/MZM_2012_92_5_a0/