Some Estimates of the Remainder in the Expressions for the Eigenvalue Asymptotics of Some Singular Integral Operators
Milutin Dostanić (1997)
Matematički Vesnik
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Milutin Dostanić (1997)
Matematički Vesnik
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Dostanić, R.Milutin, Milinković, Z.Darko (1997)
Publications de l'Institut Mathématique. Nouvelle Série
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Milutin R. Dostanić (1999)
Czechoslovak Mathematical Journal
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We find an exact asymptotic formula for the singular values of the integral operator of the form (, a Jordan measurable set) where , , and is slowly varying function with some additional properties. The formula is an explicit expression in terms of and .
Zhongxue, Lü, Hongzheng, Xie (2007)
Journal of Inequalities and Applications [electronic only]
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Dostanić, Milutin R. (1999)
Matematichki Vesnik
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Stević, Stevo (1996)
Matematichki Vesnik
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Raikov, G.D. (1999)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Dongho Chae, Gabriella Tarantello (2004)
Annales de l'I.H.P. Analyse non linéaire
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Alexey Filinovskiy (2011)
Mathematica Bohemica
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We investigate the spectral properties of the differential operator , with the Dirichlet boundary condition in unbounded domains whose boundaries satisfy some geometrical condition. Considering this operator as a self-adjoint operator in the space with the norm , we study the structure of the spectrum with respect to the parameter . Further we give an estimate of the rate of condensation of discrete spectra when it changes to continuous.