Trudy Moskovskogo Matematicheskogo Obshchestva
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Tr. Mosk. Mat. Obs., 1971, Volume 24, Pages 133–174 (Mi mmo249)  

This article is cited in 30 scientific papers (total in 30 papers)

Generalized functions and differential equations in linear spaces. I. Differentiable measures

V. I. Averbukh, O. G. Smolyanov, S. V. Fomin


Full text: PDF file (4976 kB)

Bibliographic databases:
UDC: 519.53, 517.22, 517.91
MSC: Primary 46G05; Secondary 46F10, 28A40
Received: 15.12.1969

Citation: V. I. Averbukh, O. G. Smolyanov, S. V. Fomin, “Generalized functions and differential equations in linear spaces. I. Differentiable measures”, Tr. Mosk. Mat. Obs., 24, MSU, M., 1971, 133–174

Citation in format AMSBIB
\Bibitem{AveSmoFom71}
\by V.~I.~Averbukh, O.~G.~Smolyanov, S.~V.~Fomin
\paper Generalized functions and differential equations in linear spaces. I.~Differentiable measures
\serial Tr. Mosk. Mat. Obs.
\yr 1971
\vol 24
\pages 133--174
\publ MSU
\publaddr M.
\mathnet{http://mi.mathnet.ru/mmo249}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=370184}
\zmath{https://zbmath.org/?q=an:0234.28005}


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    This publication is cited in the following articles:
    1. M. P. Kats, “Schetnaya additivnost proizvodnykh ot “dostatochno gladkikh” mer”, UMN, 28:3(171) (1973), 183–184  mathnet  mathscinet  zmath
    2. O. G. Smolyanov, “Lineinye differentsialnye operatory v prostranstvakh mer i funktsii na gilbertovom prostranstve”, UMN, 28:5(173) (1973), 251–252  mathnet  mathscinet  zmath
    3. 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
    4. A. V. Uglanov, “A result on differentiable measures on a linear space”, Math. USSR-Sb., 29:2 (1976), 217–222  mathnet  crossref  mathscinet  zmath  isi
    5. P. S. Aleksandrov, I. M. Gel'fand, A. N. Kolmogorov, E. V. Maikov, V. P. Maslov, O. A. Oleinik, Ya. G. Sinai, O. G. Smolyanov, V. M. Tikhomirov, “In memory of Sergei Vasil'evich Fomin”, Russian Math. Surveys, 31:4 (1976), 105–220  mathnet  crossref  mathscinet  zmath
    6. A. V. Uglanov, “O merakh i kharakteristicheskikh funktsionalakh na beskonechnomernykh prostranstvakh”, UMN, 32:1(193) (1977), 207–208  mathnet  mathscinet  zmath
    7. M. P. Kats, “Quasi-invariance and differentiability of measures”, Russian Math. Surveys, 33:3 (1978), 159–159  mathnet  crossref  mathscinet  zmath
    8. 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
    9. E. I. Efimova, A. V. Uglanov, “Green's formula on a Hilbert space”, Math. USSR-Sb., 47:1 (1984), 215–222  mathnet  crossref  mathscinet  zmath
    10. A. Yu. Khrennikov, “Stochastic integrals in locally convex spaces”, Russian Math. Surveys, 37:1 (1982), 166–167  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    11. Yu. L. Daletskii, “Stochastic differential geometry”, Russian Math. Surveys, 38:3 (1983), 97–125  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    12. V. I. Bogachev, “Three problems of aronszajn in measure theory”, Funct. Anal. Appl., 18:3 (1984), 242–244  mathnet  crossref  mathscinet  zmath  isi
    13. V. I. Bogachev, “Some results on differentiable measures”, Math. USSR-Sb., 55:2 (1986), 335–349  mathnet  crossref  mathscinet  zmath
    14. N. V. Norin, “An extended stochastic integral for non-Gaussian measures in locally convex spaces”, Russian Math. Surveys, 41:3 (1986), 229–230  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    15. A. Yu. Khrennikov, “Functional superanalysis”, Russian Math. Surveys, 43:2 (1988), 103–137  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    16. V. I. Bogachev, O. G. Smolyanov, “Analytic properties of infinite-dimensional distributions”, Russian Math. Surveys, 45:3 (1990), 1–104  mathnet  crossref  mathscinet  zmath  isi
    17. A. I. Kirillov, “Two mathematical problems of canonical quantization. II”, Theoret. and Math. Phys., 87:2 (1991), 447–454  mathnet  crossref  mathscinet  zmath  isi
    18. A. Yu. Khrennikov, “Generalized functions and Gaussian path integrals over non-archimedean function spaces”, Math. USSR-Izv., 39:1 (1992), 761–794  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    19. A. I. Kirillov, “Two mathematical problems of canonical quantization. III. Stochastic vacuum mechanics”, Theoret. and Math. Phys., 91:3 (1992), 591–603  mathnet  crossref  mathscinet  isi
    20. E. P. Krugova, “On the integrability of logarithmic derivatives of measures”, Math. Notes, 53:5 (1993), 506–512  mathnet  crossref  mathscinet  zmath  isi  elib
    21. A. I. Kirillov, “Prescription of measures on functional spaces by means of numerical densities and path integrals”, Math. Notes, 53:5 (1993), 555–557  mathnet  crossref  mathscinet  zmath  isi  elib
    22. N. V. Norin, O. G. Smolyanov, “Some results on logarithmic derivatives of measures on a locally convex space”, Math. Notes, 54:6 (1993), 1277–1279  mathnet  crossref  mathscinet  zmath  isi
    23. O. G. Smolyanov, M. O. Smolyanova, “Transformations of Feynman integral under some nonlinear transformations of the phase space”, Theoret. and Math. Phys., 100:1 (1994), 803–810  mathnet  crossref  mathscinet  zmath  isi
    24. A. I. Kirillov, “Infinite-dimensional analysis and quantum theory as semimartingale calculus”, Russian Math. Surveys, 49:3 (1994), 43–95  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    25. A. I. Kirillov, “On the reconstruction of measures from their logarithmic derivatives”, Izv. Math., 59:1 (1995), 121–139  mathnet  crossref  mathscinet  zmath  isi
    26. A. I. Kirillov, “Sine-Gordon type field in spacetime of arbitrary dimension. II: Stochastic quantization”, Theoret. and Math. Phys., 105:2 (1995), 1329–1345  mathnet  crossref  mathscinet  zmath  isi  elib
    27. L. Accardi, O. G. Smolyanov, M. O. Smolyanova, “Change of variable formulas for infinite-dimensional distributions”, Math. Notes, 60:2 (1996), 212–215  mathnet  crossref  crossref  mathscinet  zmath  isi
    28. H. von Weizsäcker, O. G. Smolyanov, “Formulae with logarithmic derivatives of measures related to the quantization of infinite-dimensional Hamiltonian systems”, Russian Math. Surveys, 51:2 (1996), 357–358  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    29. V. A. Romanov, “Nonequivalence of Various Definitions of Differentiability Directions for Vector Measures”, Math. Notes, 72:4 (2002), 489–494  mathnet  crossref  crossref  mathscinet  zmath  isi
    30. E. Yu. Shamarova, N. N. Shamarov, “Differential forms on locally convex spaces and the Stokes formula”, Russian Math. (Iz. VUZ), 60:8 (2016), 74–85  mathnet  crossref  isi
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