Displaying similar documents to “Essential self-adjointness of symmetric linear relations associated to first order systems”

Two separation criteria for second order ordinary or partial differential operators

Richard C. Brown, Don B. Hinton (1999)

Mathematica Bohemica

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We generalize a well-known separation condition of Everitt and Giertz to a class of weighted symmetric partial differential operators defined on domains in ℝ n . Also, for symmetric second-order ordinary differential operators we show that lim sup t → c ( p q ' ) ' / q 2 = θ < 2 where c is a singular point guarantees separation of - ( p y ' ) ' + q y on its minimal domain and extend this criterion to the partial differential setting. As a particular example it is shown that - Δ y + q y is separated on its minimal domain if q is superharmonic. For n = 1 the...

A study of an operator arising in the theory of circular plates

Leopold Herrmann (1988)

Aplikace matematiky

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The operator L 0 : D L 0 ⊂ H → H , L 0 u = 1 r d d r r d d r 1 r d d r r d u d r , D L 0 = { u ∈ C 4 ( [ 0 , R ] ) , u ' ( 0 ) = u ' ' ' ' ( 0 ) = 0 , u ( R ) = u ' ( R ) = 0 } , H = L 2 , r ( 0 , R ) is shown to be essentially self-adjoint, positive definite with a compact resolvent. The conditions on L 0 (in fact, on a general symmetric operator) are given so as to justify the application of the Fourier method for solving the problems of the types L 0 u = g and u t t + L 0 u = g , respectively.

Self-adjoint extensions by additive perturbations

Andrea Posilicano (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Let A 𝒩 be the symmetric operator given by the restriction of A to 𝒩 , where A is a self-adjoint operator on the Hilbert space ℋ and 𝒩 is a linear dense set which is closed with respect to the graph norm on D ( A ) , the operator domain of A . We show that any self-adjoint extension A Θ of A 𝒩 such that D ( A Θ ) ∩ D ( A ) = 𝒩 can be additively decomposed by the sum A Θ = A ¯ + T Θ , where both the operators A ¯ and T Θ take values in the strong dual of D ( A ) . The operator A ¯ is the closed extension of A to the whole ℋ whereas T Θ is explicitly...