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Uspekhi Mat. Nauk, 1967, Volume 22, Issue 4(136), Pages 3–54 (Mi umn5775)  

This article is cited in 39 scientific papers (total in 39 papers)

Infinite-dimensional elliptic operators and parabolic equations connected with them

Yu. L. Daletskii

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English version:
Russian Mathematical Surveys, 1967, 22:4, 1–53

Bibliographic databases:

UDC: 517.944
MSC: 35K15, 47B25, 47F05, 35Exx, 28C20, 60H20
Received: 22.08.1966

Citation: Yu. L. Daletskii, “Infinite-dimensional elliptic operators and parabolic equations connected with them”, Uspekhi Mat. Nauk, 22:4(136) (1967), 3–54; Russian Math. Surveys, 22:4 (1967), 1–53

Citation in format AMSBIB
\by Yu.~L.~Daletskii
\paper Infinite-dimensional elliptic operators and parabolic equations connected with them
\jour Uspekhi Mat. Nauk
\yr 1967
\vol 22
\issue 4(136)
\pages 3--54
\jour Russian Math. Surveys
\yr 1967
\vol 22
\issue 4
\pages 1--53

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    This publication is cited in the following articles:
    1. Yu. L. Daletskii, V. V. Stremskii, “Feinmanovskie integraly dlya uravneniya Shredingera v funktsionalnykh proizvodnykh”, UMN, 24:1(145) (1969), 191–192  mathnet  mathscinet  zmath
    2. P. M. Bleher, M. I. Vishik, “On a class of pseudodifferential operators with an infinite number of variables, and applications”, Math. USSR-Sb., 15:3 (1971), 443–491  mathnet  crossref  mathscinet  zmath
    3. M. I. Vishik, “The parametrix of elliptic operators with infinitely many independent variables”, Russian Math. Surveys, 26:2 (1971), 91–112  mathnet  crossref  mathscinet  zmath
    4. M.Ann Piech, “Some regularity properties of diffusion processes on abstract Wiener space”, Journal of Functional Analysis, 8:1 (1971), 153  crossref
    5. D.A. Dawson, “Stochastic evolution equations”, Mathematical Biosciences, 15:3-4 (1972), 287  crossref
    6. N. N. Frolov, “On the Dirichlet problem for an elliptic operator in a cylindrical domain of Hilbert space”, Math. USSR-Sb., 21:3 (1973), 423–438  mathnet  crossref  mathscinet  zmath
    7. N. N. Frolov, “On a coercive inequality for an elliptic operator in infinitely many independent variables”, Math. USSR-Sb., 19:3 (1973), 395–406  mathnet  crossref  mathscinet  zmath
    8. Hui-Hsiung Kuo, “Differential and stochastic equations in abstract Wiener space”, Journal of Functional Analysis, 12:3 (1973), 246  crossref
    9. B. L. Rozovskii, “On stochastic partial differential equations”, Math. USSR-Sb., 25:2 (1975), 295–322  mathnet  crossref  mathscinet  zmath
    10. A. V. Uglanov, “Differential equations with constant coefficients for generalized measures on Hilbert space”, Math. USSR-Izv., 9:2 (1975), 414–440  mathnet  crossref  mathscinet  zmath
    11. Yu. L. Daletskii, “Multiplikativnye operatory ot diffuzionnykh protsessov i differentsialnye uravneniya v secheniyakh vektornykh rassloenii”, UMN, 30:2(182) (1975), 209–210  mathnet  mathscinet  zmath
    12. V. I. Gorbachuk, Yu. S. Samoilenko, G. F. Us, “Spectral theory of self-adjoint operators, and infinite-dimensional analysis”, Russian Math. Surveys, 31:1 (1976), 217–231  mathnet  crossref  mathscinet  zmath
    13. Stanley L Boylan, “Fourier transforms in function-space and parabolic differential equations”, Journal of Mathematical Analysis and Applications, 56:3 (1976), 529  crossref
    14. Sergio Albeverio, Raphael Høegh-Krohn, “Dirichlet forms and diffusion processes on rigged Hilbert spaces”, Z Wahrscheinlichkeitstheorie verw Gebiete, 40:1 (1977), 1  crossref  mathscinet  zmath
    15. N. V. Krylov, B. L. Rozovskii, “On the Cauchy problem for linear stochastic partial differential equations”, Math. USSR-Izv., 11:6 (1977), 1267–1284  mathnet  crossref  mathscinet  zmath
    16. N. N. Frolov, “On the hypoellipticity of infinite-dimensional differential operators”, Math. USSR-Sb., 31:2 (1977), 269–278  mathnet  crossref  mathscinet  zmath  isi
    17. Ruth F Curtain, “Stochastic evolution equations with general white noise disturbance”, Journal of Mathematical Analysis and Applications, 60:3 (1977), 570  crossref
    18. M. I. Vishik, A. I. Komech, A. V. Fursikov, “Some mathematical problems of statistical hydromechanics”, Russian Math. Surveys, 34:5 (1979), 149–234  mathnet  crossref  mathscinet  zmath
    19. N. N. Frolov, “Self-adjointness of elliptic operators with infinitely many variables”, Funct. Anal. Appl., 14:1 (1980), 71–72  mathnet  crossref  mathscinet  zmath
    20. M. I. Vishik, A. I. Komech, “Weak solutions of the inverse Kolmogorov equation corresponding to the stochastic Navier–Stokes system”, Russian Math. Surveys, 36:3 (1981), 268–269  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    21. N. N. Frolov, “Homeomorphism of Hilbert spaces induced by a differential operator”, Funct. Anal. Appl., 15:4 (1981), 306–307  mathnet  crossref  mathscinet  zmath  isi
    22. Ya. I. Belopol'skaya, Yu. L. Daletskii, “Itô equations and differential geometry”, Russian Math. Surveys, 37:3 (1982), 109–163  mathnet  crossref  mathscinet  zmath  adsnasa
    23. A. Yu. Khrennikov, “Stochastic integrals in locally convex spaces”, Russian Math. Surveys, 37:1 (1982), 166–167  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    24. Yu. L. Daletskii, “Stochastic differential geometry”, Russian Math. Surveys, 38:3 (1983), 97–125  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    25. Wilfried Loges, “Girsanov's theorem in Hilbert space and an application to the statistics of Hilbert space- valued stochastic differential equations”, Stochastic Processes and their Applications, 17:2 (1984), 243  crossref
    26. M. N. Feller, “Infinite-dimensional elliptic equations and operators of Lévy type”, Russian Math. Surveys, 41:4 (1986), 119–170  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    27. Constantin Tudor, “On a stochastic evolution equation”, Journal of Mathematical Analysis and Applications, 122:2 (1987), 360  crossref
    28. MOSHE Marcus, VICTOR J Mize*, “Stochastic functional differential equations modelling materials with selective recall”, Stochastics, 25:4 (1988), 195  crossref
    29. Yu. V. Bagdanskii, “Cauchy problem for heat-transfer equation with irregular elliptic operator”, Ukr Math J, 41:5 (1989), 506  crossref  mathscinet
    30. S. Albeverio, Ju. G. Kondratiev, M. Röckner, “An approximate criterium of essential self-adjointness of Dirichlet operators”, Potential Anal, 1:3 (1992), 307  crossref  mathscinet  zmath
    31. V.A Liskevich, Yu.A Semenov, “Dirichlet operators: A priori estimates and the uniqueness problem”, Journal of Functional Analysis, 109:1 (1992), 199  crossref
    32. M. Asorey, “Topological phases of quantum theories. Chern–Simons theory”, Journal of Geometry and Physics, 11:1-4 (1993), 63  crossref
    33. M. Asorey, F. Falceto, J.L. López, G. Luzón, “Universality and ultraviolet regularizations of Chern–Simons theory”, Nuclear Physics B, 429:2 (1994), 344  crossref
    34. Sergio Albeverio, Anne Boutet de Monvel-Berthier, Zdzisław Brzeźniak, “Stationary phase method in infinite dimensions by finite dimensional approximations: Applications to the Schrödinger equation”, Potential Anal, 4:5 (1995), 469  crossref  mathscinet  zmath  isi
    35. V. I. Bogachev, “Differentiable measures and the Malliavin calculus”, Journal of Mathematical Sciences (New York), 87:4 (1997), 3577  crossref  mathscinet  zmath
    36. Hongwei Long, “Kato's inequality and essential self-adjointness of Dirichlet operators on certain Banach spaces”, Stochastic Analysis and Applications, 16:6 (1998), 1019  crossref
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    38. O. A. Manita, S. V. Shaposhnikov, “Nonlinear parabolic equations for measures”, St. Petersburg Math. J., 25:1 (2014), 43–62  mathnet  crossref  mathscinet  zmath  isi  elib
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