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On sharp Strichartz inequalities in low dimensions

- D. Hundertmark, V. Zharnitsky
- Mathematics
- 2006

Recently Foschi gave a proof of a sharp Strichartz inequality in one and two dimensions. In this note, a new representation in terms of an orthogonal projection operator is obtained for the space… Expand

Finite-Volume Fractional-Moment Criteria¶for Anderson Localization

- M. Aizenman, J. Schenker, R. Friedrich, D. Hundertmark
- Mathematics, Physics
- 15 October 1999

Abstract: A technically convenient signature of localization, exhibited by discrete operators with random potentials, is exponential decay of the fractional moments of the Green function within the… Expand

Lieb-Thirring Inequalities for Jacobi Matrices

- D. Hundertmark, B. Simon
- MathematicsJ. Approx. Theory
- 13 December 2001

TLDR

A sharp bound for an eigenvalue moment of the one-dimensional Schrödinger operator

- D. Hundertmark, E. Lieb, L. Thomas
- Mathematics
- 18 June 1998

We give a proof of the Lieb-Thirring inequality in the critical case d=1, γ = 1/2, which yields the best possible constant.

A short introduction to Anderson localization

- D. Hundertmark
- Mathematics
- 2007

We give short introduction to some aspects of the theory of Anderson localization.

Heat-flow monotonicity of Strichartz norms

- Jonathan Bennett, N. Bez, A. Carbery, D. Hundertmark
- Mathematics
- 27 September 2008

Most notably we prove that for $d=1,2$ the classical Strichartz norm $$\|e^{i s\Delta}f\|_{L^{2+4/d}_{s,x}(\mathbb{R}\times\mathbb{R}^d)}$$ associated to the free Schr\"{o}dinger equation is… Expand

Continuity properties of Schrödinger semigroups with magnetic fields

- K. Broderix, D. Hundertmark, H. Leschke
- Mathematics
- 13 August 1998

The objects of the present study are one-parameter semigroups generated by Schrodinger operators with fairly general electromagnetic potentials. More precisely, we allow scalar potentials from the… Expand

Variational Estimates for Discrete Schrödinger Operators with Potentials of Indefinite Sign

- D. Damanik, D. Hundertmark, R. Killip, B. Simon
- Mathematics
- 11 November 2002

AbstractLet H be a one-dimensional discrete Schrödinger operator. We prove that if Σess(H)⊂[−2,2], then H−H0 is compact and Σess(H)=[−2,2]. We also prove that if ${{H_0 + \frac 14 V^2}}$ has at least… Expand

A diamagnetic inequality for semigroup differences

- D. Hundertmark, B. Simon
- Mathematics
- 7 January 2004

The diamagnetic inequality for the magnetic Schrodinger semigroup is extended to the difference of the semigroups of magnetic Schrodinger operators with Neumann and Dirichlet boundary conditions on… Expand

New bounds on the Lieb-Thirring constants

- D. Hundertmark, A. Laptev, T. Weidl
- Mathematics
- 16 June 1999

Abstract.Improved estimates on the constants Lγ,d, for 1/2<γ<3/2, d∈N, in the inequalities for the eigenvalue moments of Schrödinger operators are established.

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