Parabolic equations associated with the number operator

Piech, M. Ann

doi:10.1090/S0002-9947-1974-0350231-3

Parabolic equations associated with the number operator
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Trans. Amer. Math. Soc. 194 (1974), 213-222 Request permission

Abstract:

We study existence and uniqueness of solutions of the Cauchy problem for $\dot u = Nu$ where N is the number operator on abstract Wiener space.

References

Victor Goodman, A divergence theorem for Hilbert space, Trans. Amer. Math. Soc. 164 (1972), 411–426. MR 298417, DOI 10.1090/S0002-9947-1972-0298417-9
Victor Goodman, Quasi-differentiable functions of Banach spaces, Proc. Amer. Math. Soc. 30 (1971), 367–370. MR 284811, DOI 10.1090/S0002-9939-1971-0284811-3
Leonard Gross, Measurable functions on Hilbert space, Trans. Amer. Math. Soc. 105 (1962), 372–390. MR 147606, DOI 10.1090/S0002-9947-1962-0147606-6
Leonard Gross, Abstract Wiener spaces, Proc. Fifth Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif., 1965/66) Univ. California Press, Berkeley, Calif., 1967, pp. 31–42. MR 0212152
Leonard Gross, Potential theory on Hilbert space, J. Functional Analysis 1 (1967), 123–181. MR 0227747, DOI 10.1016/0022-1236(67)90030-4
Seizô Itô, The fundamental solution of the parabolic equation in a differentiable manifold, Osaka Math. J. 5 (1953), 75–92. MR 56178
Hui Hsiung Kuo, Stochastic integrals in abstract Wiener space, Pacific J. Math. 41 (1972), 469–483. MR 306435, DOI 10.2140/pjm.1972.41.469
H. J. Landau and L. A. Shepp, On the supremum of a Gaussian process, Sankhyā Ser. A 32 (1970), 369–378. MR 286167
H. P. McKean, Geometry of differential space, Ann. Probability 1 (1973), 197–206. MR 353471, DOI 10.1214/aop/1176996973
Edward Nelson, An existence theorem for second order parabolic equations, Trans. Amer. Math. Soc. 88 (1958), 414–429. MR 95341, DOI 10.1090/S0002-9947-1958-0095341-4
Edward Nelson, Dynamical theories of Brownian motion, Princeton University Press, Princeton, N.J., 1967. MR 0214150, DOI 10.1515/9780691219615

Quantum fields and Markoff fields

M. Ann Piech, A fundamental solution of the parabolic equation on Hilbert space. II. The semigroup property, Trans. Amer. Math. Soc. 150 (1970), 257–286. MR 278116, DOI 10.1090/S0002-9947-1970-0278116-8
M. Ann Piech, Differential equations on abstract Wiener space, Pacific J. Math. 43 (1972), 465–473. MR 320559, DOI 10.2140/pjm.1972.43.465
Irving Segal, Construction of non-linear local quantum processes. I, Ann. of Math. (2) 92 (1970), 462–481. MR 272306, DOI 10.2307/1970628

On the theory of Brownian motion

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Yasuo Umemura, On the infinite dimensional Laplacian operator, J. Math. Kyoto Univ. 4 (1964/65), 477–492. MR 180872, DOI 10.1215/kjm/1250524602