Transmutation and separation of variables

References

• Braaksma , B. . A Singular Cauchy Problem and Generalized Translations, Int. Conf. Diff. . pp. 40 – 52 . N.Y. : Academic Press .
   Google Scholar
• Bragg , L. 1974 . Linear evolution equations that involve products of commutative operators . SIAM Jour. Math. Anal , 5 : 327 – 335 .
   Google Scholar
• Bragg , L. 1974 . Related nonhomogeneous partial differential equations. . Applicable Anal , 4 : 161 – 189 .
   Google Scholar
• Bragg , L. and Dettman , J. 1968 . An operator calculus for related partial differential equations . Jour. Math. Anal. Appl , 22 : 261 – 271 .
   Google Scholar
• Bragg , L. and Dettman , J. 1968 . Related partial differential equations and their applications . SIAM Jour. Appl. Math. , 16 : 459 – 467 .
   Google Scholar
• Carroll , R. 1976 . Singular Cauchy problems in symmetric spaces. . Jour. Math. Anal. Appl , 16 : 41 – 54 .
   Google Scholar
• Carroll , R. 1978 . The group theoretic nature of certain recursion relations for singular Cauchy problems. . Jour. Math. Anal. Appl , 63
   Google Scholar
• Carroll , R. 1979 . “ Operational calculus and abstract differential equations ” . In Notas de Matematica , North-Holland .
   Google Scholar
• Carroll , R. and Showalter , R. 1976 . Singular and Degenerate Cauchy Problems , N.Y. : Academic Press .
   Google Scholar
• Copson , E. and Erdelyi , A. 1958 . On a partial differential equation with two singular lines . Arch. Rat. Mech. Anal , 2 : 76 – 86 .
   Google Scholar
• Delsarte , J. 1938 . C.R. Acad. Set Paris , 206 : 1780 – 1782 .
   Google Scholar
• Delsarte , J. and Lions , J. 1957 . Transmutations d'opérateurns différentiels dans le domaine complexe . Comm. Math Helv , 32 : 113 – 128 .
   Google Scholar
• 1954 . Bateman manuscript project. Tables of integral transforms , N.Y. : McGraw- Hill .
   Google Scholar
• Hersh , R. 1975 . The method of transmutation. Partial diff. egs. and related topics . Springer Lect. Notes , 446 : 264 – 282 . N.Y
   Google Scholar
• Levitan , B. 1949 . The application of generalized displacement operators to linear differential equations of the second order . Uspekhi Mat. Nauk, SSSR , 4 : 3 – 112 .
   Google Scholar
• Levitan , B. and Lions , J. 1956 . Op´rateurs de Delsarte et probl´mes mixtes . Bull Soc. Math. France , 84 : 9 – 95 .
   Google Scholar
• Lions , J. 1962 . Equations Differentielles-Operationnelles , Berlin : Springer .
   Google Scholar
• Lions , J. 1959 . Opérateurs de transmutation singuliers et équations d'Euler-Poisson-Darboux généralisées . Rend. Sem. Mat. Fis. Milano , 28 : 3 – 16 .
   Google Scholar
• Magnus , W. , Oberhettinger , F. and Soni , R. Formulas and Theorems for the Special Functions of Mathematical Physics
   Google Scholar
• Marienko , V. 1952 . Some questions in the theory of one dimensional linear differential operators of the second order . Trudy Mask. Mat. Obcs , 1 : 327 – 420 . 2 (1953), 3-82.
   Google Scholar
• Mercer , A. 1962 . On integral transform pairs arising from second order differential equations . Proc. Edinburgh Math. Soc , 13 : 63 – 68 .
   Google Scholar
• Mercer , A. 1963 . On integral transform pairs arising from differential equations of any even order . Quart. Jour. Math. Oxford , 14 : 9 – 15 .
   Google Scholar
• Mercer , A. 1964 . A theory of integral transforms . Quart. Jour. Math. Oxford , 15 : 149 – 154 .
   Google Scholar
• Mercer , A. 1948 . Differential equations of Sturm-Liouville type on a half axis. . Mat. Sbornik , 23 : 3 – 52 .
   Google Scholar
• Sansone , G. 1959 . Orthogonal Functions , Interscience-wiley .
   Google Scholar
• Thyssen , M. 1957 . Opérateurs de Delsarte particuliers. . Bull. Soc. Roy. Sci. Liege , 26 : 87 – 96 .
   Google Scholar
• Thyssen , M. 1961 . Sur certains opérateurs de transmutation particuliers . Mem. Soc. Roy. Sci. Liege , 6 : 7 – 32 .
   Google Scholar
• Titchmarsh , E. The Theory of Fourier Integrals
   Google Scholar
• Titchmarsh , E. Eigenfunction Expansions Associated with Second Order Differential Equations
   Google Scholar
• Zemanian , A. 1968 . Generalized Integral Transforms , N.Y. : Interscience-Wiley .
   Google Scholar