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Semiclassical asymptotics for a class of singular Schrödinger operators

Frank, Rupert L. and Larson, Simon (2020) Semiclassical asymptotics for a class of singular Schrödinger operators. . (Unpublished)

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Let Ω ⊂ ℝ^d be bounded with C¹ boundary. In this paper we consider Schrödinger operators −Δ + W on Ω with W(x) ≈ dist(x,∂Ω)⁻² as dist(x,∂Ω) → 0. Under weak assumptions on W we derive a two-term asymptotic formula for the sum of the eigenvalues of such operators.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper
Frank, Rupert L.0000-0001-7973-4688
Larson, Simon0000-0002-0057-8211
Additional Information:We are deeply grateful to Ari Laptev for sharing his fascination for spectral estimates and Hardy’s inequality with us and we would like to dedicate this paper to him on the occasion of his 70th birthday. U.S. National Science Foundation grants DMS-1363432 and DMS-1954995 (R.L.F.) and Knut and Alice Wallenberg Foundation grant KAW 2018.0281 (S.L.) are acknowledged.
Funding AgencyGrant Number
Knut and Alice Wallenberg Foundation2018.0281
Subject Keywords:Schrödinger operator, Semiclassical asymptotics
Classification Code:Mathematics Subject Classification 2020. Primary 35P20
Record Number:CaltechAUTHORS:20211004-222658897
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:111198
Deposited By: George Porter
Deposited On:04 Oct 2021 22:56
Last Modified:04 Oct 2021 22:56

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