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. I*, Interscience Publishers, Inc., New York, N.Y., 1953. MR**0065391****[2]**George D. Birkhoff,*Boundary value and expansion problems of ordinary linear differential equations*, Trans. Amer. Math. Soc.**9**(1908), no. 4, 373–395. MR**1500818**, https://doi.org/10.1090/S0002-9947-1908-1500818-6**[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. Naĭmark,*Investigation of the spectrum and the expansion in eigenfunctions of a non-selfadjoint differential operator of the second order on a semi-axis*, Amer. Math. Soc. Transl. (2)**16**(1960), 103–193. MR**0117382****[5]**Earl A. Coddington and Norman Levinson,*Theory of ordinary differential equations*, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955. MR**0069338****[6]**Bernard Friedman,*Principles and techniques of applied mathematics*, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1956. MR**0079181****[7]**Konrad Knopp,*Theory of Functions. II. Applications and Continuation of the General Theory*, Dover Publications, New York, 1947. MR**0019722****[8]**Philip M. Morse and Herman Feshbach,*Methods of theoretical physics. 2 volumes*, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1953. MR**0059774****[9]**J. Schwartz,*Perturbations of spectral operators, and applications. I. Bounded perturbations*, Pacific J. Math.**4**(1954), 415–458. MR**0063568****[10]**M. Machover,*Generalized eigenvectors and separation of variables*, Doctoral Dissertation, New York Univ., New York, 1963.**[11]**Henry P. Kramer,*Perturbation of differential operators*, Pacific J. Math.**7**(1957), 1405–1435. MR**0092059**

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

Article copyright:
© Copyright 1965
American Mathematical Society