On the Eigenvalues of a Class of Integral Equations Arising in Laser Theory

Previous article Next article On the Eigenvalues of a Class of Integral Equations Arising in Laser TheoryHarry HochstadtHarry Hochstadthttps://doi.org/10.1137/1008005PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] L. Bergstein and , H. Schachter, Resonant modes of optic interferometer cavities, I. Plane-parallel end reflections, J. Opt. Soc. Amer., 54 (1964), 887–903 CrossrefISIGoogle Scholar[2] A. G. Fox and , T. Li, Resonant modes in a maser interferometer, Bell System Tech. J., 40 (1961), 453–488 CrossrefISIGoogle Scholar[3] Frigyes Riesz and , Béla Sz.-Nagy, Functional analysis, Frederick Ungar Publishing Co., New York, 1955xii+468 MR0071727 0070.10902 Google Scholar[4] I. Fredholm, Sur une classe d'équations fonctionelles, Acta Math., 27 (1903), 365–390 CrossrefGoogle Scholar[5] D. J. Newman and , S. P. Morgan, Existence of eigenvalues of a class of integral equations arising in laser theory, Bell System Tech. J., 43 (1964), 113–126 0173.14301 CrossrefISIGoogle Scholar[6] J. Alan Cochran, The existence of eigenvalues for the integral equations of laser theory, Bell System Tech. J., 44 (1965), 77–88 MR0171137 0131.10702 CrossrefISIGoogle Scholar[7] Ralph Philip Boas, Jr., Entire functions, Academic Press Inc., New York, 1954x+276 MR0068627 0058.30201 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails On the r-nuclearity of some integral operators on Lebesgue spacesTohoku Mathematical Journal, Vol. 67, No. 1 Cross Ref The Fox–Li Operator as a Test and a Spur for Wiener–Hopf Theory11 June 2012 Cross Ref Nonorthogonal Optical Modes and Resonators Cross Ref IV Unstable Resonator Modes Cross Ref Solution of the eigenvalue problem of an integral equation with the help of its associated differential equation applied to the calculation of diffraction losses in confocal resonatorsJournal of Mathematical Physics, Vol. 26, No. 10 Cross Ref The converging prolate spheroidal functions and their use in Fresnel opticsOptics Communications, Vol. 45, No. 1 Cross Ref Analytic variational method for determining the modes of marginally stable resonators1 December 1980 | Journal of the Optical Society of America, Vol. 70, No. 12 Cross Ref Resonant-mode analysis of single-mode face pumped lasers1 April 1977 | Applied Optics, Vol. 16, No. 4 Cross Ref Degrees of freedom of an optical image in coherent illumination, in the presence of aberrations1 May 1975 | Journal of the Optical Society of America, Vol. 65, No. 5 Cross Ref Eigensystems Associated with the Complex-Symmetric Kernels of Laser TheoryJames Alan Cochran and Erold W. Hinds12 July 2006 | SIAM Journal on Applied Mathematics, Vol. 26, No. 4AbstractPDF (921 KB)Existence of Eigenvalues of Integral EquationsR. D. Russell and L. F. Shampine18 July 2006 | SIAM Review, Vol. 13, No. 2AbstractPDF (807 KB)Spatial Coherence in Periodic Systems*1 November 1966 | Journal of the Optical Society of America, Vol. 56, No. 11 Cross Ref Laser beams and resonatorsProceedings of the IEEE, Vol. 54, No. 10 Cross Ref Laser Beams and Resonators1 October 1966 | Applied Optics, Vol. 5, No. 10 Cross Ref Volume 8, Issue 1| 1966SIAM Review History Submitted:01 February 1965Published online:18 July 2006 InformationCopyright © 1966 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1008005Article page range:pp. 62-65ISSN (print):0036-1445ISSN (online):1095-7200Publisher:Society for Industrial and Applied Mathematics