Boundary Value Problems for Operator Differential Equations

Горбачук, Василь; Горбачук, М. Л.

doi:10.1007/978-94-011-3714-0

Cited by 540 publications

(703 citation statements)

References 6 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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“…This is of course a (if not "the") standard example for boundary relations, see [GG84] and the references therein. Formulated in our present language it reads as follows.…”

Section: Appendix a Some Examplesmentioning

confidence: 94%

Spectral Multiplicity of Selfadjoint Schrödinger Operators on Star-Graphs with Standard Interface Conditions

Simonov¹,

Woracek

2013

Integr. Equ. Oper. Theory

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We analyze the singular spectrum of selfadjoint operators which arise from pasting a finite number of boundary relations with a standard interface condition. A model example for this situation is a Schrödinger operator on a star-shaped graph with continuity and Kirchhoff conditions at the interior vertex. We compute the multiplicity of the singular spectrum in terms of the spectral measures of the Weyl functions associated with the single (independently considered) boundary relations. This result is a generalization and refinement of a Theorem of I.S.Kac.

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“…Then A 0 is a self-adjoint extension of S (due to the general properties of boundary triplets [9]). Moreover, it follows from (2.7) and Remark 2.13 that A 0 ∈ Υ.…”

Section: The Resolvent Formulamentioning

confidence: 99%

On self-adjoint operators in Krein spaces constructed by Clifford algebra Cl_2

Kuzhel¹,

Patsyuck²

2012

OpMath

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Abstract. Let J and R be anti-commuting fundamental symmetries in a Hilbert space H. The operators J and R can be interpreted as basis (generating) elements of the complex Clifford algebra Cl2(J, R) := span{I, J, R, iJR}. An arbitrary non-trivial fundamental symmetry from Cl2(J, R) is determined by the formula J α = α1J + α2R + α3iJR, where α ∈ S 2 . Let S be a symmetric operator that commutes with Cl2(J, R). The purpose of this paper is to study the sets ΣJ α (∀ α ∈ S 2 ) of self-adjoint extensions of S in Krein spaces generated by fundamental symmetries J α (J α -self-adjoint extensions). We show that the sets ΣJ α and ΣJ β are unitarily equivalent for different α, β ∈ S 2 and describe in detail the structure of operators A ∈ ΣJ α with empty resolvent set.

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Boundary Value Problems for Operator Differential Equations

Cited by 540 publications

References 6 publications

Selfadjoint extensions of a singular differential operator

Selfadjoint extensions of a singular differential operator

Spectral Multiplicity of Selfadjoint Schrödinger Operators on Star-Graphs with Standard Interface Conditions

On self-adjoint operators in Krein spaces constructed by Clifford algebra Cl_2

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