• Corpus ID: 237491585

Counterexample to the Laptev--Safronov conjecture

@inproceedings{Bogli2021CounterexampleTT,
  title={Counterexample to the Laptev--Safronov conjecture},
  author={Sabine Bogli and Jean-Claude Cuenin},
  year={2021}
}
We prove that the Laptev–Safronov conjecture (Comm. Math. Phys. 2009) is false in the range that is not covered by Frank’s positive result (Bull. Lond. Math. Soc. 2011). The simple counterexample is adaptable to a large class of Schrödinger type operators, for which we also prove new sharp upper bounds. 
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References

SHOWING 1-10 OF 49 REFERENCES
Improved Eigenvalue Bounds for Schrödinger Operators with Slowly Decaying Potentials
We extend a result of Davies and Nath (J Comput Appl Math 148(1):1–28, 2002) on the location of eigenvalues of Schrödinger operators with slowly decaying complex-valued potentials to higher
Eigenvalue bounds for Schrödinger operators with complex potentials
We show that the absolute values of non-positive eigenvalues of Schrodinger operators with complex potentials can be bounded in terms of L_p-norms of the potential. This extends an inequality of
Uniform bounds of discrete Birman–Schwinger operators
In this note, uniform bounds of the Birman-Schwinger operators in the discrete setting are studied. For uniformly decaying potentials, we obtain the same bound as in the continuous setting. However,
Eigenvalue bounds for Dirac and fractional Schr\"odinger operators with complex potentials
We prove Lieb-Thirring-type bounds for fractional Schr\"odinger operators and Dirac operators with complex-valued potentials. The main new ingredient is a resolvent bound in Schatten spaces for the
On the smooth Feshbach-Schur map
A new variant of the Feshbach map, called smooth Feshbach map, has been introduced recently by Bach et al., in connection with the renormalization analysis of non-relativistic quantum
Limiting absorption principle onLp-spaces and scattering theory
In this paper, we study the mapping property form Lp to Lq of the resolvent of the Fourier multiplier operators and scattering theory of generalized Schrodinger operators. Though the first half of
Trace ideals and their applications
Preliminaries Calkin's theory of operator ideals and symmetrically normed ideals convergence theorems for $\mathcal J_P$ Trace, determinant, and Lidskii's theorem $f(x)g(-i\nabla)$ Fredholm theory
Eigenvalue bounds for non-self-adjoint Schrödinger operators with nontrapping metrics
We prove weighted uniform estimates for the resolvent of the Laplace operator in Schatten spaces, on non-trapping asymptotically conic manifolds of dimension $n\ge 3$, generalizing a result of Frank
A note on eigenvalue bounds for Schrödinger operators
We obtain a new bound on the location of eigenvalues for a non-self-adjoint Schr\"odinger operator with complex-valued potentials by obtaining a weighted $L^2$ estimate for the resolvent of the
Modern Fourier Analysis
Preface.- Smoothness and Function Spaces.- BMO and Carleson Measures.- Singular Integrals of Nonconvolution Type.- Weighted Inequalities.- Boundedness and Convergence of Fourier Integrals.-
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2
3
4
5
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