Spectral Analysis of Differential Operators

Rofe-Beketov, F. S.; Kholkin, Aleksandr M

doi:10.1142/5788

Cited by 59 publications

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“…The general theory of selfadjoint extensions of symmetric operators in any Hilbert space and their spectral theory tall and well-built have been investigated by many mathematicians ( [4][5][6][7] ). Applications of this theory to two point differential operators in Hilbert space of functions are continied today even.…”

Section: Introductionmentioning

confidence: 99%

Selfadjoint extensions of a singular differential operator

2011

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Section: Introductionmentioning

confidence: 99%

Selfadjoint extensions of a singular differential operator

2011

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“…Note that this distribution, under the presence of multiple poles for the resolvent, does not reduce to a matrix measure even in the non-selfadjoint case. These results are applied to extending the Sturm type oscillation theory from selfadjoint systems [10] to systems with triangular matrix potentials [1].…”

Section: Dedicated To Our Teacher Academician Vladimir a Marchenko mentioning

confidence: 99%

“…with C(x, t) being the Cauchy function that in each variable satisfies equation (10) and the initial conditions…”

Section: Dedicated To Our Teacher Academician Vladimir a Marchenko mentioning

confidence: 99%

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On Spectrum of Differential Operator with Block-Triangular Matrix Coefficients

Kholkin¹,

Rofe-Beketov²

2014

Z. mat. fiz. anal. geom.

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For the Sturm-Louville equation with block-triangular matrix potential that increases at infinity, both increasing and decreasing at infinity matrix solutions are found. The structure of spectrum for the differential operator with these coefficients is defined.Key words: differential operator, spectrum, block-triangular matrix coefficients.Mathematics Subject Classification 2010: 34K11, 47A10. Dedicated to our Teacher, Academician Vladimir A. Marchenko on the occasion of his 90th birthday, with appreciation and admiration for his contribution to spectral theory, differential equations and mathematical physicsThe study of the relationship between spectral and oscillation properties of non-selfadjoint differential operators with block-triangular matrix coefficients that increase at infinity [1] includes the study of the structure of the spectra of these operators. For the case of an operator with decreasing at infinity triangular matrix potential and a bounded first moment, the structure of the spectrum in the context of the inverse scattering problem was established in [2][3][4].In [5,6], V.A. Marchenko introduced a notion of the generalized spectral function R for a Sturm-Liouville operator with arbitrary complex valued potential on the semiaxis. This result was generalized to the case of non-selfadjoint systems [7,8]. The distribution (the matrix one in the case of systems) acts on c A.M. Kholkin and F.S. Rofe-Beketov, 2014

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“…It is known that the general theory of extension of densely de…ned linear operators in Hilbert spaces was initiated by J. von Neumann in his seminal work [17] in 1929 (for more detail analysis see [18]). Later in 1949 and 1952 M.I.…”

Section: Introductionmentioning

confidence: 99%