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Accurate eigenvalue asymptotics for the magnetic Neumann Laplacian

Soeren Fournais, Bernard Helffer (2006)

Annales de l’institut Fourier

Motivated by the theory of superconductivity and more precisely by the problem of the onset of superconductivity in dimension two, many papers devoted to the analysis in a semi-classical regime of the lowest eigenvalue of the Schrödinger operator with magnetic field have appeared recently. Here we would like to mention the works by Bernoff-Sternberg, Lu-Pan, Del Pino-Felmer-Sternberg and Helffer-Morame and also Bauman-Phillips-Tang for the case of a disc. In the present paper we settle one important...

Accurate Spectral Asymptotics for periodic operators

Victor Ivrii (1999)

Journées équations aux dérivées partielles

Asymptotics with sharp remainder estimates are recovered for number 𝐍 ( τ ) of eigenvalues of operator A ( x , D ) - t W ( x , x ) crossing level E as t runs from 0 to τ , τ → ∞ . Here A is periodic matrix operator, matrix W is positive, periodic with respect to first copy of x and decaying as second copy of x goes to infinity, E either belongs to a spectral gap of A or is one its ends. These problems are first treated in papers of M. Sh. Birman, M. Sh. Birman-A. Laptev and M. Sh. Birman-T. Suslina.

Adaptive wavelet methods for saddle point problems

Stephan Dahlke, Reinhard Hochmuth, Karsten Urban (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Recently, adaptive wavelet strategies for symmetric, positive definite operators have been introduced that were proven to converge. This paper is devoted to the generalization to saddle point problems which are also symmetric, but indefinite. Firstly, we investigate a posteriori error estimates and generalize the known adaptive wavelet strategy to saddle point problems. The convergence of this strategy for elliptic operators essentially relies on the positive definite character of the operator....

Additive combinations of special operators

Pei Wu (1994)

Banach Center Publications

This is a survey paper on additive combinations of certain special-type operators on a Hilbert space. We consider (finite) linear combinations, sums, convex combinations and/or averages of operators from the classes of diagonal operators, unitary operators, isometries, projections, symmetries, idempotents, square-zero operators, nilpotent operators, quasinilpotent operators, involutions, commutators, self-commutators, norm-attaining operators, numerical-radius-attaining operators, irreducible operators...

Addresses

(1979)

Abstracta. 7th Winter School on Abstract Analysis

Adjoint bi-continuous semigroups and semigroups on the space of measures

Bálint Farkas (2011)

Czechoslovak Mathematical Journal

For a given bi-continuous semigroup ( T ( t ) ) t ≥ 0 on a Banach space X we define its adjoint on an appropriate closed subspace X ∘ of the norm dual X ' . Under some abstract conditions this adjoint semigroup is again bi-continuous with respect to the weak topology σ ( X ∘ , X ) . We give the following application: For Ω a Polish space we consider operator semigroups on the space C b ( Ω ) of bounded, continuous functions (endowed with the compact-open topology) and on the space M ( Ω ) of bounded Baire measures (endowed with the weak * -topology)....

Adjoint characterisations of unbounded weakly compact, weakly completely continuous and unconditionally converging operators

T. Alvarez, R. Cross, A. Gouveia (1995)

Studia Mathematica

Characterisations are obtained for the following classes of unbounded linear operators between normed spaces: weakly compact, weakly completely continuous, and unconditionally converging operators. Examples of closed unbounded operators belonging to these classes are exhibited. A sufficient condition is obtained for the weak compactness of T' to imply that of T.

Currently displaying 901 – 920 of 1501