The Wiener integral and perturbation theory of the Schrödinger operator
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- by Donald Babbitt PDF
- Bull. Amer. Math. Soc. 70 (1964), 254-259
References
- J. L. Doob, Stochastic processes, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1953. MR 0058896
- R. K. Getoor, Additive functionals of a Markov process, Pacific J. Math. 7 (1957), 1577–1591. MR 94850, DOI 10.2140/pjm.1957.7.1577
- R. K. Getoor, Markov operators and their associated semi-groups, Pacific J. Math. 9 (1959), 449–472. MR 107297, DOI 10.2140/pjm.1959.9.449
- Einar Hille and Ralph S. Phillips, Functional analysis and semi-groups, American Mathematical Society Colloquium Publications, Vol. 31, American Mathematical Society, Providence, R.I., 1957. rev. ed. MR 0089373
- Teruo Ikebe and Tosio Kato, Uniqueness of the self-adjoint extension of singular elliptic differential operators, Arch. Rational Mech. Anal. 9 (1962), 77–92. MR 142894, DOI 10.1007/BF00253334
- Mark Kac, Probability and related topics in physical sciences, Lectures in Applied Mathematics (Proceedings of the Summer Seminar, Boulder, Colorado, vol. 1957, Interscience Publishers, London-New York, 1959. With special lectures by G. E. Uhlenbeck, A. R. Hibbs, and B. van der Pol. MR 0102849
- Tosio Kato, Quadratic forms in Hilbert spaces and asymptotic perturbation series, University of California, Department of Mathematics, Berkeley, Calif., 1955. MR 0073958
- Edward Nelson, Feynman integrals and the Schrödinger equation, J. Mathematical Phys. 5 (1964), 332–343. MR 161189, DOI 10.1063/1.1704124
- Daniel Ray, On spectra of second-order differential operators, Trans. Amer. Math. Soc. 77 (1954), 299–321. MR 66539, DOI 10.1090/S0002-9947-1954-0066539-2
- Frigyes Riesz and Béla Sz.-Nagy, Functional analysis, Frederick Ungar Publishing Co., New York, 1955. Translated by Leo F. Boron. MR 0071727 11. F. Rellich, Perturbation theory of eigenvalue problems, Lecture Notes, New York University, New York, 1955.
- E. C. Titchmarsh, Eigenfunction Expansions Associated with Second-Order Differential Equations, Oxford, at the Clarendon Press, 1946 (German). MR 0019765
Additional Information
- Journal: Bull. Amer. Math. Soc. 70 (1964), 254-259
- DOI: https://doi.org/10.1090/S0002-9904-1964-11106-X
- MathSciNet review: 0161180