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19 Dec 2022: With respect to the standard complex structure, there are N families of smooth holomorphicdiscs of index 2, and they are all Fredholm regular.

22 Jul 2022: MATHEMATICS OF COMPUTATIONVolume 89, Number 322, March 2020, Pages 737–766https://doi.org/10.1090/mcom/3475. Article electronically published on September 12, 2019. PSEUDOERGODIC OPERATORS. AND PERIODIC BOUNDARY CONDITIONS. MATTHEW J. COLBROOK.

29 Jan 2022: The common way to solve this Fredholm integral equation of the second kind is to use theiteration scheme under the assumption α 1 with f = f0 as initial guess [20].

15 Oct 2021: b) Compactness Weak compactness for Hilbert spaces; Rellich-Kondrachov theorem;Fredholm alternative; spectrum of L; spectral theorem for symmetric (formally self-adjoint) elliptic BVPs.

19 Apr 2021: the Fredholm determinant for small fluctuations about the classical solution. However, in this case the nonzero eigenvalues cancel between bosons and.

6 Dec 2020: σess(T) = {z C : T zI is not Fredholm}, ress(T) = sup{|z| : z σess(T)}.

23 Sep 2020: royalsocietypublishing.org/journal/rspa. ResearchCite this article: Colbrook MJ, Kisil AV. 2020 AMathieu function boundary spectral methodfor scattering by multiple variable poro-elasticplates, with applications to metamaterials andacoustics.

15 Jun 2020: COMPUTING SPECTRA - ON THE SOLVABILITY COMPLEXITY INDEX HIERARCHYAND TOWERS OF ALGORITHMS. J. BEN-ARTZI, M. J. COLBROOK, A. C. HANSEN, O. NEVANLINNA, AND M. SEIDEL. 1. INTRODUCTION. This paper resolves the long-standing computational spectral problem

30 Aug 2019: Part III, Paper 15. 3. 3. (i) Define Fredholm map, Fredholm operator, Fredholm index. ... iii) Prove that s As is Fredholm.[You may quote the Closed Range Lemma without proof].

30 Aug 2019: 2. 1. (a) Define what is meant by a Fredholm operator of index n on Hilbert space. ... b) Show that an operator is Fredholm if and only if it is invertible modulo thecompact operators.