Generalized eigenvectors and separation of variables

Author:
Maurice Machover

Journal:
Trans. Amer. Math. Soc. **115** (1965), 505-524

MSC:
Primary 35.75

DOI:
https://doi.org/10.1090/S0002-9947-1965-0194740-3

MathSciNet review:
0194740

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References | Similar Articles | Additional Information

**[1]**R. Courant and D. Hilbert,*Methods of mathematical physics*, Vol. 1, Chapter 5, Interscience, New York, 1953. MR**0065391 (16:426a)****[2]**G. D. Birkhoff,*Boundary value and expansion problems of ordinary linear differential equations*, Trans. Amer. Math. Soc.**9**(1908), 373-395. MR**1500818****[3]**J. D. Tamarkin,*Some general problems of the theory of ordinary linear differential equations and expansions of an arbitrary function in a series of fundamental functions*, Math. Z.**27**(1927), 1-54.**[4]**M. A. Naimark,*Investigation of the spectrum and the expansion in eigenfunctions of a non-selfadjoint differential operator of the second order on a semi-axis*, Trudy Moskov. Mat. Obšč.**3**(1954), 181-270; English transl., Amer. Math. Soc. Transl. (2)**16**(1960), 103-193. MR**0117382 (22:8162)****[5]**E. A. Coddington and N. Levinson,*Theory of ordinary differential equations*, Chapters 7, 11, and 12, McGraw-Hill, New York, 1955. MR**0069338 (16:1022b)****[6]**B. Friedman,*Principles and techniques of applied mathematics*, Chapters 4, 5, and Theorem 2.11, Applied Mathematics Series, Wiley, New York, 1956. MR**0079181 (18:43a)****[7]**K. Knopp,*Theory of functions*. II, Dover, New York, 1947. MR**0019722 (8:452e)****[8]**P. M. Morse and H. Feshbach,*Methods of theoretical physics*. I, Chapter 5, International Series in Pure and Applied Physics, McGraw-Hill, New York, 1953. MR**0059774 (15:583h)****[9]**J. Schwartz,*Perturbations of spectral operators and applications*, Pacific J. Math.**4**(1954), 415-458. MR**0063568 (16:144b)****[10]**M. Machover,*Generalized eigenvectors and separation of variables*, Doctoral Dissertation, New York Univ., New York, 1963.**[11]**H. P. Kramer,*Perturbation of differential operators*, Pacific J. Math.**7**(1957), 1405-1434. MR**0092059 (19:1054d)**

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DOI:
https://doi.org/10.1090/S0002-9947-1965-0194740-3

Article copyright:
© Copyright 1965
American Mathematical Society