Depending on the behaviour of complex-valued electromagnetic potential in neighbourhood infinity, pseudomodes one-dimensional Dirac operators corresponding to large pseudoeigenvalues are constructed. This is a first systematic approach which goes beyond standard semi-classical setting. Furthermore, this results substantial progress achieving optimal conditions and conclusions as well covering w...

Let L be a self-adjoint invertible operator in Hilbert space such that − 1 is p -summable. Under certain discrete dimension spectrum assumption on , we study the relation between (regularized) Fredholm determinant, det ( I + z ⋅ ) one hand and zeta regularized ζ other. One of main results formula = exp ⁡ ∑ j ! d log | 0 . We show derivatives can expressed terms values heat trace coefficients Fu...