We obtain L p eigenfunction bounds for the harmonic oscillator H=-Δ+x^2 H=-Δ+ x 2 in R^n
ℝ n and for other related operators, improving earlier results of Thangavelu and of …

We discuss the eigenvalues $ E_j $ of Schrödinger operators $-\Delta+ V $ in $ L^ 2
(\mathbb {R}^ d) $ with complex potentials $ V\in L^ p $, $ p<\infty $. We show that (A) …

We use a straightforward variation on a recent argument of Hezari and Rivière [8] to obtain
localized L p-estimates for all exponents larger than or equal to the critical exponent pc= 2 …

If 12 is an open set in R", and if N (£ l, X) is the number of eigenvalues of-A (with Dirichlet
boundary conditions on d£ 2) which are< X (k> 0), one has the asymptotic formula of Weyl …

On negative eigenvalues of two-dimensional Schrödinger operators Page 1 Proc. London
Math. Soc. (3) 108 (2014) 441–483 Cо2013 London Mathematical Society doi:10.1112/plms/pdt036 …

We show that the absolute values of non-positive eigenvalues of Schrödinger operators with
complex potentials can be bounded in terms of L p-norms of the potential. This extends an …

On the Lieb-Thirring Constants LΊJ\ for y^ Page 1 Commun. Math. Phys. 178, 135-146 (1996)
Communications IΠ Mathematical Physics © Springer-Verlag 1996 On the Lieb-Thirring …

We give a short proof of the CLR bound on the number of negative eigenvalues of
Schrödinger operators. The argument, which is based on work of Rumin, leads to …

Eigenvalue Estimates for Schrödinger Operators with Complex Potentials Page 1 Digital Object
Identifier (DOI) 10.1007/s00220-009-0883-4 Commun. Math. Phys. 292, 29–54 (2009) …

Let Ω Ω be a bounded open domain in R^ n R n with smooth boundary and X=(X_1, X_2, ...,
X_m) X=(X 1, X 2,…, X m) be a system of real smooth vector fields defined on Ω Ω with the …