2005/12/16 by H. Falomir, H Falomir, P. A. G. Pisani +1
Mathematics · Physics and Astronomy · #Asymptotic expansion #Boundary (topology) #Bounded function #Differential operator #Generalization #Holomorphic and Operator Theory #Integer (computer science) #Operator (biology) #Random Matrices and Applications #Singularity #Spectral Theory in Mathematical Physics #TRACE (psycholinguistics) #math-ph #math.MP #msc:34L05 #msc:34L40 #msc:81Q10
paper · pdf · doi:10.1088/0305-4470/39/21/s25
published as J.Phys. A39 (2006) 6333-6340 · Submitted to Journal of Physics A, special issue corresponding to QFEXT'05, The Seventh Workshop on Quantum Field Theory under the Influence of External Conditions; IEEC, CSIC and University of Barcelona. Barcelona, Spain, 5-9 September 2005 (9 pages.)
arxiv created 2005/12/16 · openalex publication_date 2006/05/10 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We get a generalization of Krein's formula—which relates the resolvents of different self-adjoint extensions of a differential operator with regular coefficients—to the non-regular case A = −∂ 2 x + (ν 2 − 1/4)/ x 2 + V ( x ), where 0 < ν < 1, and V ( x ) is an analytic function of bounded from below. We show that the trace of the heat kernel e − tA admits a non-standard small- t asymptotic expansion which contains, in general, integer powers of t ν . In particular, these powers are present for those self-adjoint extensions of A which are characterized by boundary conditions that break the local formal scale invariance at the singularity.