Feynman-Kac functionals and positive solutions of \(1/2 \Delta u+qu=0\). (English) Zbl 0496.60078


60J45 Probabilistic potential theory
60J65 Brownian motion
31A30 Biharmonic, polyharmonic functions and equations, Poisson’s equation in two dimensions
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[1] Aizenman, M.; Simon, B., Brownian motion and Harnack inequality for Schrödinger operators, Comm. Pure Appl. Math., 35, 209-273 (1982) · Zbl 0459.60069
[2] Chung, K.L.: An inequality for boundary value problems, preprint · Zbl 0528.60071
[3] Chung, K.L., Li, Peter: Comparison of probability and eigenvalue methods for the Schrödinger equation. Advances in Math. (to appear) · Zbl 0608.60061
[4] Chung, K. L.; Rao, K. M.; Cinlar, E.; Chung, K. L.; Getoor, R. K., Feynman-Kac functional and the Schrödinger equation, Seminar on Stochastic Process (1981), Boston: BirkhÄuser, Boston · Zbl 0492.60073
[5] Doob, J. L., Semimartingales and subharmonic functions, Trans. Amer. Math. Soc., 77, 86-121 (1954) · Zbl 0059.12205
[6] Doob, J. L., Conditional Brownian motion and the boundary limits of harmonic functions, Bull. Soc. Math. France, 85, 431-458 (1957) · Zbl 0097.34004
[7] Hunt, R. A.; Wheeden, R. L., Positive harmonic functions on Lipschitz domains, Trans. Amer. Math. Soc., 147, 507-527 (1970) · Zbl 0193.39601
[8] Khas’minskii, R. Z., On positive solutions of the equation Au+Vu=0, Theory Probab. Appl., 4, 309-318 (1959) · Zbl 0089.34501
[9] Meyer, P.-A., Processus de Markov, Lecture Notes in Math. 26 (1967), Berlin Heidelberg New York: Springer, Berlin Heidelberg New York · Zbl 0189.51403
[10] Port, S. C.; Stone, C. J., Brownian Motion and Classical Potential Theory (1978), New York: Academic Press, New York · Zbl 0413.60067
[11] Rao, Murali: Brownian motion and classical potential theory. Aarhus Universitet, Matematisk Institut. Lecture Notes Series, no. 47. (1977) · Zbl 0345.31001
[12] Widman, K.-O., Inequalities for the Green function and boundary continuity of the gradient of solutions of elliptic differential equations, Math. Scand., 21, 17-37 (1967) · Zbl 0164.13101
[13] Williams, R.J.: A Feynman-Kac gauge for solvability of the Schrödinger equation. Adv. Appl. Math. (to appear) · Zbl 0565.35104
[14] Zygmund, A., Trigonometric Series (1959), Cambridge: Cambridge University Press, Cambridge · Zbl 0085.05601
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