Journal of Mathematical Chemistry

, Volume 55, Issue 6, pp 1253–1277 | Cite as

Zero interval limit perturbation expansion for the spectral entities of Hilbert–Schmidt operators combined with most dominant spectral component extraction: formulation and certain technicalities

Original Paper


A perturbation-expansion-at-zero-interval-limit based numeric al algorithm to calculate the eigenpairs of Hilbert–Schmidt integral operators having symmetric kernels is developed in the present work. We have developed the perturbation expansion only for the most dominant eigenvalue and relevant eigenfunction. The less important eigenpairs have been determined by using the most dominant spectral component extraction recursively over the kernel restrictions. The main lines of the formulation and certain related technicalities are presented here. The confirmation of the presented theory via certain illustrative implementations and the convergence discussion for the obtained perturbation series as well as the numerical comparison with some mostly considered methods are given in the next companion of this paper.


Hilbert–Schmidt integral operators Perturbation expansions Eigenvalues Eigenfunctions Singular value decomposition for continuous functions Most dominant spectral component extraction 

Mathematics Subject Classification

45B05 45F10 45P05 47A55 65D15 


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Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.Informatics Instituteİstanbul Technical UniversityMaslakTurkey

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