Computation of the eigenvalues of Fredholm–Stieltjes integral equations

References

• Mikhlin , SG . 1964 . Integral Equations and Their Applications , 2nd Edn , Oxford : Pergamon Press .
   Google Scholar
• Zaanen , AC . 1953 . Linear Analysis. Measure and Integral, Banach and Hilbert Space, Linear Integral Equations , New York : Interscience Publ. Inc. . Amsterdam: North Holland Publ. Co.; Noordhoff, N.V. Groningen: P.
   Google Scholar
• Anselone , PM . 1971 . Collectively Compact Operator Approximation Theory and Application to Integral Equations, Prentice-Hall Series in Automatic Computation , Englewood Cliffs, NJ : Prentice-Hall, Inc. .
   Google Scholar
• Miranda , C . 1992 . “ Opere Scelte ” . In Opere dei Grandi Matematici Italiani , Edited by: Spagnolo , S , Lanconelli , E , Sbordone , C and Trombetti , G . Roma : Cremonese .
   Google Scholar
• Miranda , C. 1938/40 . Alcune generalizzazioni delle serie di funzioni ortogonali e loro applicazioni . Rendiconti del Seminario Matematico – Universitá e Politecnico di Torino , 7 : 5 – 17 .
   Google Scholar
• Jung , IH , Kwon , KH , Lee , DW and Littlejohn , LL . 1995 . Sobolev orthogonal polynomials and spectral differential equations . Transactions of the American Mathematical Society , 347 : 3629 – 3643 .
   Google Scholar
• Marcellán , F , Pérez , TE , Piñar , MA and Ronveaux , A . 1996 . General Sobolev orthogonal polynomials . Journal of Mathematical Analysis and Applications , 200 : 614 – 634 .
   Google Scholar
• Duhamel , J . 1843 . Les vibrations d'une corde flessible chargé d'un ou de plusieurs curseurs . Journal of École Polytecnique , XVII : 1 – 36 .
   Google Scholar
• Lord Rayleigh . 1894 . The Theory of Sound , Vol. 1 , 200 London : Macmillan & Co. .
   Google Scholar
• Kneser , A . 1914 . Belastete Integralgleichungen . Rendiconti del Circolo Matematico di Palermo , XXXVII : 169 – 197 .
   Google Scholar
• Teichmann , J . 1919 . Mechanische Probleme die auf Belastete Integralgleichungen führen , Breslau : Dissertation Universität .
   Google Scholar
• Fichera , G . 1973 . Abstract and Numerical Aspects of Eigenvalue Theory, Lecture Notes , Edmonton : Dept. of Math., The University of Alberta .
   Google Scholar
• Fichera , G . 1978 . Numerical and Quantitative Analysis, Surveys and Reference Works in Mathematics , London : Pitman, Boston, Mass .
   Google Scholar
• Natalini , P , Noschese , S and Ricci , PE . 1999 . An iterative method for computing the eigenvalues of second kind Fredholm operators and applications . Proceedings International Workshop on “Orthogonal Polynomials: Numerical and Symbolic Algorithms”, Leganés (Madrid) , 9 : 128 – 136 . 1998, in E.T.N.A
   Google Scholar
• Widder , DV . 1999 . Advanced Calculus , 3rd Edn , New York : Dover Publ. Inc. .
   Google Scholar
• Baker , CTH . 1977 . The Numerical Treatment of Integral Equations , Oxford, UK : Claredon Press .
   Google Scholar
• Delves , LM and Mohamed , JL . 1985 . Computational Methods for Integral Equations , Cambridge, UK : Cambridge University Press .
   Google Scholar
• Stummel , F and Heiner , K . 1980 . Introduction to Numerical Analysis , Edinburgh : Scottish Academic Press .
   Google Scholar
• Krall , G . 1970 . Meccanica Tecnica delle Vibrazioni , Vol. 1 , Roma : Veschi .
   Google Scholar
• Hochstadt , H . 1973 . Integral Equations, Pure & Applied Mathematics , New York, London : Wiley Interscience Publication .
   Google Scholar
• Krasnov , M , Kiselev , A and Makarenko , G . 1971 . Problems and Exercises in Integral Equations , Moscow : MIR .
   Google Scholar