ar X iv : m at h / 98 03 12 9 v 1 [ m at h . SP ] 2 6 M ar 1 99 8 SEMI - CLASSICAL STATES FOR NON - SELF - ADJOINT SCHRÖDINGER OPERATORS

ar X iv : h ep - t h / 98 12 18 6 v 1 2 1 D ec 1 99 8 Yangians , finite W - algebras and the Non Linear Schrödinger hierarchy

ar X iv : m at h / 98 03 04 6 v 1 [ m at h . PR ] 1 1 M ar 1 99 8 LOCAL FIELDS , GAUSSIAN MEASURES , AND BROWNIAN MOTIONS Steven

ar X iv : m at h / 99 10 08 9 v 1 [ m at h . SP ] 1 8 O ct 1 99 9 ON LOCAL BORG - MARCHENKO UNIQUENESS RESULTS

We provide a new short proof of the following fact, first proved by one of us in 1998: If two Weyl-Titchmarsh m-functions, m j (z), of two Schrödinger operators H j = − d 2 dx 2 + q j , j = 1, 2 in L 2 ((0, R)), 0 < R ≤ ∞, are exponentially close, that is, |m 1 (z) − m 2 (z)| = |z|→∞ O(e −2 Im(z 1/2)a), 0 < a < R, then q 1 = q 2 a.e. on [0, a]. The result applies to any boundary conditions at x...

ar X iv : 0 90 5 . 09 74 v 1 [ m at h - ph ] 7 M ay 2 00 9 Symmetries and resonance sets for δ ′ - interactions July 20 , 2009

The symmetry properties of the family of δ ′-interactions with a resonant non-zero transparency resulting in non-separated states are discussed. It is shown that the connection matrix for these physically motivated interactions and the corresponding family of self-adjoint extensions can be constructed in a self-consistent way if the product δ ′ (x)ψ(x), where ψ(x) is a discontinuous wavefunctio...

ar X iv : m at h / 06 02 06 9 v 1 [ m at h . SP ] 4 F eb 2 00 6 SEMICLASSICAL NON - CONCENTRATION NEAR HYPERBOLIC ORBITS

For a large class of semiclassical pseudodifferential operators, including Schrödinger operators, P (h) = −h∆g + V (x), on compact Riemannian manifolds, we give logarithmic lower bounds on the mass of eigenfunctions outside neighbourhoods of generic closed hyperbolic orbits. More precisely we show that if A is a pseudodifferential operator which is microlocally equal to the identity near the hy...