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31,141
On rank one H−3perturbations of positive selfadjoint operators
 413–422, CMS CONF. PROC
, 2000
"... Rank one H−3 perturbations of positive self–adjoint operators are constructed using a certain extended Hilbert space and regularization procedures. Applications to Schrödinger operators with point interactions are discussed. ..."
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Cited by 8 (4 self)
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Rank one H−3 perturbations of positive self–adjoint operators are constructed using a certain extended Hilbert space and regularization procedures. Applications to Schrödinger operators with point interactions are discussed.
Grounding in communication
 In
, 1991
"... We give a general analysis of a class of pairs of positive selfadjoint operators A and B for which A + XB has a limit (in strong resolvent sense) as h10 which is an operator A, # A! Recently, Klauder [4] has discussed the following example: Let A be the operator(d2/A2) + x2 on L2(R, dx) and let ..."
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Cited by 1122 (20 self)
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We give a general analysis of a class of pairs of positive selfadjoint operators A and B for which A + XB has a limit (in strong resolvent sense) as h10 which is an operator A, # A! Recently, Klauder [4] has discussed the following example: Let A be the operator(d2/A2) + x2 on L2(R, dx) and let
Diagonals of selfadjoint operators
"... Abstract. The eigenvalues of a selfadjoint n×n matrix A can be put into a decreasing sequence λ = (λ1,..., λn), with repetitions according to multiplicity, and the diagonal of A is a point of R n that bears some relation to λ. The SchurHorn theorem characterizes that relation in terms of a system ..."
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Cited by 11 (1 self)
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properties of selfadjoint operators in II1 factors to their images under a conditional expectation onto a maximal abelian subalgebra. 1. Preface These are research notes that are not intended for publication in their present form. They summarize some of the results of a project begun by the authors
Stability of coupled second order equations.
"... In [13], D. L. Russell considered a linear oscillator in a Hilbert space H represented in the form u′′(t) +Au(t) = h (1) where A is a (generally unbounded) positive selfadjoint operator on H. He ..."
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In [13], D. L. Russell considered a linear oscillator in a Hilbert space H represented in the form u′′(t) +Au(t) = h (1) where A is a (generally unbounded) positive selfadjoint operator on H. He
High Order Singular Rank One Perturbations of a Positive Operator
 INTEGRAL EQUATIONS AND OPERATOR THEORY
, 2005
"... In this paper selfadjoint realizations in Hilbert and Pontryagin spaces of the formal expression Lα = L + α 〈 · , ϕ〉ϕ are discussed and compared. Here L is a positive selfadjoint operator in a Hilbert space H with inner product 〈 · , · 〉, α is a real parameter, and ϕ in the rank one perturbat ..."
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Cited by 4 (0 self)
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In this paper selfadjoint realizations in Hilbert and Pontryagin spaces of the formal expression Lα = L + α 〈 · , ϕ〉ϕ are discussed and compared. Here L is a positive selfadjoint operator in a Hilbert space H with inner product 〈 · , · 〉, α is a real parameter, and ϕ in the rank one
Integral Equations and Operator Theory High Order Singular Rank One Perturbations of a Positive Operator
"... Abstract. In this paper selfadjoint realizations in Hilbert and Pontryagin spaces of the formal expression Lα = L + α 〈 · , ϕ〉ϕ are discussed and compared. Here L is a positive selfadjoint operator in a Hilbert space H with inner product 〈 · , · 〉, α is a real parameter, and ϕ in the rank one p ..."
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Abstract. In this paper selfadjoint realizations in Hilbert and Pontryagin spaces of the formal expression Lα = L + α 〈 · , ϕ〉ϕ are discussed and compared. Here L is a positive selfadjoint operator in a Hilbert space H with inner product 〈 · , · 〉, α is a real parameter, and ϕ in the rank one
Positive forms on Banach spaces
 Acta Math. Hungar
"... The first representation theorem establishes a correspondence between positive, selfadjoint operators and closed, positive forms on Hilbert spaces. The aim of this paper is to show that some of the results remain true if the underlying space is a reflexive Banach space. In particular, the construct ..."
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Cited by 3 (0 self)
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The first representation theorem establishes a correspondence between positive, selfadjoint operators and closed, positive forms on Hilbert spaces. The aim of this paper is to show that some of the results remain true if the underlying space is a reflexive Banach space. In particular
Analyticity spaces of selfadjoint operators subjected to perturbations with applications to Hankel invariant distribution spaces
 SIAM J. Math. Anal
"... by S.J.L. van Eijndhoven and J. de Graaf A new theory of generalized functions has been developed by one of the authors (De Graaf). In this theory the analyticity domain of each positive selfadjoint unbounded operator A in a Hilbert space X is regarded as a test space denoted by SX,A. In the first ..."
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by S.J.L. van Eijndhoven and J. de Graaf A new theory of generalized functions has been developed by one of the authors (De Graaf). In this theory the analyticity domain of each positive selfadjoint unbounded operator A in a Hilbert space X is regarded as a test space denoted by SX,A. In the first
On the spectral asymptotics of operators on manifolds with ends
 Abstr. Appl. Anal. (2013), Art. ID 909782
"... We deal with the asymptotic behaviour, for → +∞, of the counting function ( ) of certain positive selfadjoint operators P with double order ( , ), , > 0, ̸ = , defined on a manifold with ends M. The structure of this class of noncompact manifolds allows to make use of calculi of pseudodifferent ..."
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We deal with the asymptotic behaviour, for → +∞, of the counting function ( ) of certain positive selfadjoint operators P with double order ( , ), , > 0, ̸ = , defined on a manifold with ends M. The structure of this class of noncompact manifolds allows to make use of calculi
INEQUALITIES FOR NORMS OF SOME INTEGRAL OPERATORS
 MATH. INEQUALITIES AND APPLIC. 1,N2, (1998), 259265
, 1998
"... Let (A(a)u)(x): = � a 0 (1 − xt)−1 u(t) dt, 0 < a < 1. Properties of the operators A(a) as a → 1 are studied. It is proved that A: = A(1) is a bounded, positive selfadjoint operator in H = L 2 [0, 1], A  ≤ π, while A: C(0, 1) → C(0, 1) is unbounded. ..."
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Let (A(a)u)(x): = � a 0 (1 − xt)−1 u(t) dt, 0 < a < 1. Properties of the operators A(a) as a → 1 are studied. It is proved that A: = A(1) is a bounded, positive selfadjoint operator in H = L 2 [0, 1], A  ≤ π, while A: C(0, 1) → C(0, 1) is unbounded.
Results 1  10
of
31,141