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On PovznerWienholtzType SelfAdjointness Results For MatrixValued SturmLiouville Operators
 Proc. Math. Soc. Edinburgh 133A
, 2003
"... We derive PovznerWienholtztype selfadjointness results for m m matrixvalued SturmLiouville operators T = R dx + Q in ((a; b); Rdx) , m 2 N, for (a; b) a halfline or R. ..."
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Cited by 7 (3 self)
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We derive PovznerWienholtztype selfadjointness results for m m matrixvalued SturmLiouville operators T = R dx + Q in ((a; b); Rdx) , m 2 N, for (a; b) a halfline or R.
The form sum and the Friedrichs extension of Schrödingertype operators on Riemannina manifolds
 Proc. Amer. Math. Soc
, 2004
"... Abstract. We considerHV = ∆M+V, where (M, g) is a Riemannian manifold (not necessarily complete), and ∆M is the scalar Laplacian on M. We assume that V = V0 + V1, where V0 ∈ L2loc(M) and −C ≤ V1 ∈ L1loc(M) (C is a constant) are realvalued, and ∆M + V0 is semibounded below on C∞c (M). Let T0 be the ..."
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Cited by 2 (1 self)
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Abstract. We considerHV = ∆M+V, where (M, g) is a Riemannian manifold (not necessarily complete), and ∆M is the scalar Laplacian on M. We assume that V = V0 + V1, where V0 ∈ L2loc(M) and −C ≤ V1 ∈ L1loc(M) (C is a constant) are realvalued, and ∆M + V0 is semibounded below on C∞c (M). Let T0 be the Friedrichs extension of (∆M + V0)C∞c (M). We prove that the form sum T0+̃V1, coincides with the selfadjoint operator TF associated to the closure of the restriction to C∞c (M) × C∞c (M) of the sum of two closed quadratic forms of T0 and V1. This is an extension of a result of Cycon. The proof adopts the scheme of Cycon, but it requires the use of a more general version of Kato’s inequality for operators on Riemannian manifolds.
Twobody quantum mechanical problem on spheres
, 2005
"... The quantum mechanical twobody problem with a central interaction on the sphere S n is considered. Using recent results in representation theory an ordinary differential equation for some energy levels is found. For several interactive potentials these energy levels are calculated in explicit form. ..."
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The quantum mechanical twobody problem with a central interaction on the sphere S n is considered. Using recent results in representation theory an ordinary differential equation for some energy levels is found. For several interactive potentials these energy levels are calculated in explicit form.
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"... Abstract. We describe classical and recent results on the spectral theory of Schrödinger and Pauli operators with singular electric and magnetic potentials ..."
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Abstract. We describe classical and recent results on the spectral theory of Schrödinger and Pauli operators with singular electric and magnetic potentials
ftp ejde.math.txstate.edu (login: ftp) A PROPERTY OF SOBOLEV SPACES ON COMPLETE RIEMANNIAN MANIFOLDS
"... Abstract. Let (M, g) be a complete Riemannian manifold with metric g and the Riemannian volume form dν. We consider the R kvalued functions T ∈ [W −1,2 (M) ∩ L 1 loc (M)]k and u ∈ [W 1,2 (M)] k on M, where [W 1,2 (M)] k is a Sobolev space on M and [W −1,2 (M)] k is its dual. We give a sufficient c ..."
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Abstract. Let (M, g) be a complete Riemannian manifold with metric g and the Riemannian volume form dν. We consider the R kvalued functions T ∈ [W −1,2 (M) ∩ L 1 loc (M)]k and u ∈ [W 1,2 (M)] k on M, where [W 1,2 (M)] k is a Sobolev space on M and [W −1,2 (M)] k is its dual. We give a sufficient condition for the equality of 〈T, u 〉 and the integral of (T · u) over M, where 〈·, · 〉 is the duality between [W −1,2 (M)] k and [W 1,2 (M)] k. This is an extension to complete Riemannian manifolds of a result of H. Brézis and F. E. Browder. 1. Introduction and
POSITIVE PERTURBATIONS OF SELFADJOINT SCHRÖDINGER OPERATORS ON RIEMANNIAN MANIFOLDS
"... Abstract. We consider a Schrödinger differential expression L0 = ∆M+V0 on a (not necessarily complete) Riemannian manifold (M, g) with metric g, where ∆M is the scalar Laplacian on M and V0 is a realvalued locally square integrable function on M. We consider a perturbation L0 + V, where V is a no ..."
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Abstract. We consider a Schrödinger differential expression L0 = ∆M+V0 on a (not necessarily complete) Riemannian manifold (M, g) with metric g, where ∆M is the scalar Laplacian on M and V0 is a realvalued locally square integrable function on M. We consider a perturbation L0 + V, where V is a nonnegative locally squareintegrable function on M, and give sufficient conditions for L0 + V to be essentially selfadjoint on C c (M). This is an extension of a result of T. Kappeler. The proof adopts Kappeler’s technique, but requires the use of positivity preserving property of resolvents of certain selfadjoint operators in L2(M).
On maccretive Schrödinger operators in Lpspaces on manifolds of bounded geometry
"... Let (M, g) be a manifold of bounded geometry with metric g. We consider a Schrödingertype differential expression H = ∆M + V, where ∆M is the scalar Laplacian on M and V is a nonnegative locally integrable function on M. We give a sufficient condition for H to have an maccretive realization in t ..."
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Let (M, g) be a manifold of bounded geometry with metric g. We consider a Schrödingertype differential expression H = ∆M + V, where ∆M is the scalar Laplacian on M and V is a nonnegative locally integrable function on M. We give a sufficient condition for H to have an maccretive realization in the space Lp(M), where 1 < p < +∞. The proof uses Kato’s inequality and Lptheory of elliptic operators on Riemannian manifolds. Key words: manifold of bounded geometry, maccretive, Schrödinger operator, PACS: 58J50, 35P05 1 Introduction and the main results Let (M, g) be a C ∞ Riemannian manifold without boundary, with metric g = (gjk) and dimM = n. We will assume that M is connected and oriented. By dµ we will denote the Riemannian volume element of M. In what follows, by T ∗xM and T
Comment.Math.Univ.Carolinae 45,1 (2004)91–100 91 On
"... msectorial Schrödingertype operators with singular potentials on manifolds of bounded geometry ..."
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msectorial Schrödingertype operators with singular potentials on manifolds of bounded geometry
ftp ejde.math.swt.edu (login: ftp) SELFADJOINTNESS OF SCHRÖDINGERTYPE OPERATORS WITH SINGULAR POTENTIALS ON MANIFOLDS OF BOUNDED GEOMETRY
"... Abstract. We consider the Schrödinger type differential expression ..."
Comment.Math.Univ.Carolin. 45,1 (2004)91–100 91 On
"... msectorial Schrödingertype operators with singular potentials on manifolds of bounded geometry ..."
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msectorial Schrödingertype operators with singular potentials on manifolds of bounded geometry