RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor
Subscription
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Uspekhi Mat. Nauk:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Uspekhi Mat. Nauk, 1967, Volume 22, Issue 6(138), Pages 201–260 (Mi umn5813)  

This article is cited in 54 scientific papers (total in 54 papers)

The theory of differentiation in linear topological spaces

V. I. Averbukh, O. G. Smolyanov


Full text: PDF file (6781 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 1967, 22:6, 201–258

Bibliographic databases:

MSC: 46A04, 46A11, 46G05, 26A24, 26Cxx
Received: 30.11.1966

Citation: V. I. Averbukh, O. G. Smolyanov, “The theory of differentiation in linear topological spaces”, Uspekhi Mat. Nauk, 22:6(138) (1967), 201–260; Russian Math. Surveys, 22:6 (1967), 201–258

Citation in format AMSBIB
\Bibitem{AveSmo67}
\by V.~I.~Averbukh, O.~G.~Smolyanov
\paper The theory of differentiation in linear topological spaces
\jour Uspekhi Mat. Nauk
\yr 1967
\vol 22
\issue 6(138)
\pages 201--260
\mathnet{http://mi.mathnet.ru/umn5813}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=223886}
\zmath{https://zbmath.org/?q=an:0195.42601|0312.46054}
\transl
\jour Russian Math. Surveys
\yr 1967
\vol 22
\issue 6
\pages 201--258
\crossref{https://doi.org/10.1070/RM1967v022n06ABEH003761}


Linking options:
  • http://mi.mathnet.ru/eng/umn5813
  • http://mi.mathnet.ru/eng/umn/v22/i6/p201

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. I. Averbukh, O. G. Smolyanov, “The various definitions of the derivative in linear topological spaces”, Russian Math. Surveys, 23:4 (1968), 67–113  mathnet  crossref  mathscinet  zmath
    2. D. S. Salko, “K teorii neyavnykh funktsii v lokalno-vypuklykh prostranstvakh”, UMN, 24:2(146) (1969), 235–236  mathnet  mathscinet  zmath
    3. P. Enflo, “Uniform structures and square roots in topological groups”, Isr J Math, 8:3 (1970), 253  crossref  mathscinet  zmath
    4. H. Ratschek, G. Schröder, “Über die Ableitung von intervallwertigen Funktionen”, Computing, 7:3-4 (1971), 172  crossref  mathscinet  zmath
    5. Yamamuro S., “On the semigroup of Hadamard differentiable mappings”, J. Austral. Math. Soc., 14:3 (1972), 329  crossref  mathscinet  zmath
    6. Lloyd J.W., Yamamuro S., “Inductive and projective limits of smooth topological vector spaces”, Bull. Austral. Math. Soc., 6:2 (1972), 227  crossref  mathscinet  zmath
    7. A. S. Nemirovskii, S. M. Semenov, “On polynomial approximation of functions on Hilbert space”, Math. USSR-Sb., 21:2 (1973), 255–277  mathnet  crossref  mathscinet  zmath
    8. Lloyd J., “Two topics in the differential calculus on topological linear spaces”, Bull. Austral. Math. Soc., 9:2 (1973), 305  crossref
    9. V. M. Scherbin, “Strogaya differentsiruemost otobrazhenii $K$-prostranstv i nekotorye teoremy o lokalnoi obratimosti”, UMN, 30:4(184) (1975), 269–270  mathnet  mathscinet  zmath
    10. V. P. Fedotov, “Differentsirovanie v topologicheskikh gruppakh”, UMN, 31:5(191) (1976), 255–256  mathnet  mathscinet  zmath
    11. M. F. Sukhinin, “On the differentiability with respect to the initial condition of a solution to an ordinary differential equation”, Math. USSR-Sb., 35:1 (1979), 115–129  mathnet  crossref  mathscinet  zmath  isi
    12. Ekkehard Sachs, “Differentiability in optimization theory1”, Mathematische Operationsforschung und Statistik. Series Optimization, 9:4 (1978), 497  crossref
    13. G. I. Nazin, “Topological structure of the family of solutions of the Bogolyubov equation”, Theoret. and Math. Phys., 42:2 (1980), 159–166  mathnet  crossref  mathscinet  isi
    14. Fitzpatrick S., “Metric projections and the differentiability of distance functions”, Bull. Austral. Math. Soc., 22:2 (1980), 291  crossref  mathscinet  zmath
    15. J-B. Hiriart-Urruty, “Mean value theorems in nonsmooth analysis”, Numerical Functional Analysis and Optimization, 2:1 (1980), 1  crossref
    16. Vincent J. Bruno, “The continuity of increasing polynomial operators on ordered topological vector spaces”, Nonlinear Analysis: Theory, Methods & Applications, 4:4 (1980), 815  crossref
    17. V. Yu. Ventkus, “Analyticity of Gaussian Measures”, Theory Probab Appl, 27:1 (1982), 155  crossref  mathscinet  isi
    18. E.P Hamilton, M.Z Nashed, “Global and local variational derivatives and integral representations of Gâteaux differentials”, Journal of Functional Analysis, 49:1 (1982), 128  crossref
    19. Martin Schechter, “Differentiation in abstract spaces”, Journal of Differential Equations, 55:3 (1984), 330  crossref
    20. W. Esty, R. Gillette, M. Hamilton, D. Taylor, “Asymptotic distribution theory of statistical functionals: The compact derivative approach for robust estimators”, Ann Inst Statist Math, 37:1 (1985), 109  crossref  mathscinet  zmath  isi
    21. V. V. Vedenyapin, “Differential forms in spaces without a norm. A theorem on the uniqueness of Boltzmann's $H$-function”, Russian Math. Surveys, 43:1 (1988), 193–219  mathnet  crossref  mathscinet  zmath  adsnasa
    22. A. Yu. Khrennikov, “Functional superanalysis”, Russian Math. Surveys, 43:2 (1988), 103–137  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    23. Sharp B., “New directions in convex analysis: the differentiability of convex functions on topological linear spaces”, Bull. Austral. Math. Soc., 41:2 (1990), 333  crossref  zmath  isi
    24. Sharp B., “The differentiability of convex functions on topological linear spaces”, Bull. Austral. Math. Soc., 42:2 (1990), 201–213  crossref  mathscinet  zmath  isi
    25. Alexander Shapiro, “Asymptotic analysis of stochastic programs”, Ann Oper Res, 30:1 (1991), 169  crossref  mathscinet  zmath
    26. M.Z. Nashed, E.P. Hamilton, “Local and global bivariational gradients and singular variational derivatives of functionals on Cn[a,b]”, Nonlinear Analysis: Theory, Methods & Applications, 17:9 (1991), 841  crossref
    27. Roberto Luiz Soraggi, “The -problem for a (0, 2)-form in a D.F.N. space”, Journal of Functional Analysis, 98:2 (1991), 380  crossref
    28. S. G. Lobanov, “Picard's theorem for ordinary differential equations in locally convex spaces”, Russian Acad. Sci. Izv. Math., 41:3 (1993), 465–487  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    29. 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
    30. Roberto Luiz Soraggi, “Local Factorization of Differential Forms on Fréchet–Schwartz Spaces”, Journal of Mathematical Analysis and Applications, 209:2 (1997), 365  crossref
    31. A. I. Gerko, “Asymptotically recurrent solutions to $\beta$-differential equations”, Math. Notes, 67:6 (2000), 707–717  mathnet  crossref  crossref  mathscinet  zmath  isi
    32. A. D. Ioffe, “Metric regularity and subdifferential calculus”, Russian Math. Surveys, 55:3 (2000), 501–558  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    33. V. Bentkus, F. Götze, “Lattice points in multidimensional bodies”, form, 13:2 (2001), 149  crossref  mathscinet  zmath  isi
    34. Jian-Jian Ren, Pranab Kumar Sen, “Second Order Hadamard Differentiability in Statistical Applications”, Journal of Multivariate Analysis, 77:2 (2001), 187  crossref
    35. S. Ya. Serovaǐskiǐ, “Approximate Solution of Singular Optimization Problems”, Math. Notes, 74:5 (2003), 685–694  mathnet  crossref  crossref  mathscinet  zmath  isi
    36. S. Ya. Serovaǐskiǐ, “Approximate solution of optimization problems for infinite-dimensional singular systems”, Siberian Math. J., 44:3 (2003), 519–528  mathnet  crossref  mathscinet  zmath  isi
    37. Tsoy-Wo Ma, “Holomorphic manifolds on locally convex spaces”, Analys in Theo Applic, 21:4 (2005), 339  crossref  mathscinet  zmath
    38. S. Ya. Serovaǐskiǐ, “A control problem in coefficients and an extended derivative with respect to a convex set”, Russian Math. (Iz. VUZ), 49:12 (2005), 43–51  mathnet  mathscinet  elib
    39. S. Ya. Serovaǐskiǐ, “Optimal control in nonlinear infinite-dimensional systems with nondifferentiability of two types”, Math. Notes, 80:6 (2006), 833–847  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    40. S. Ya. Serovaǐskiǐ, “Sequential derivatives of operators and their applications in nonsmooth problems of optimal control”, Russian Math. (Iz. VUZ), 50:12 (2006), 73–84  mathnet  mathscinet
    41. K. A. Rybakov, I. L. Sotskova, “An optimal control for random-structure nonlinear systems under incomplete state vector information”, Autom. Remote Control, 67:7 (2006), 1070–1081  mathnet  crossref  mathscinet  zmath  elib  elib
    42. S. Ya. Serovaiskii, “Differentiation of operators and optimality conditions in category interpretation”, Russian Math. (Iz. VUZ), 54:2 (2010), 57–65  mathnet  crossref  mathscinet  zmath  elib
    43. S. Ya. Serovaiskii, “The necessary optimality conditions for a nonlinear stationary system whose state functional is not differentiable with respect to the control”, Russian Math. (Iz. VUZ), 54:6 (2010), 26–38  mathnet  crossref  mathscinet  elib
    44. P. Vojčák, “A Characterization of Hyers–Lang Differentiability in Terms of a Tangent Cone”, Math. Notes, 89:2 (2011), 214–223  mathnet  crossref  crossref  mathscinet  isi
    45. Korennoi A.V., Mezhuev A.M., “Optimalnye algoritmy filtratsii nemarkovskikh protsessov”, Radiotekhnika, 2011, no. 2, 09–16  elib
    46. T. Konderla, “A Construction of Convex Functions”, Math. Notes, 91:1 (2012), 65–68  mathnet  crossref  crossref  mathscinet  isi  elib
    47. V. I. Averbukh, T. Konderla, “Continuous Convex $\mathrm{MS}$-Differentiable Function Need not Be $\mathrm{HL}$-Differentiable”, Math. Notes, 91:2 (2012), 153–160  mathnet  crossref  crossref  mathscinet  isi  elib
    48. Benjamin Doyon, “Calculus on manifolds of conformal maps and CFT”, J. Phys. A: Math. Theor, 45:31 (2012), 315202  crossref
    49. K. A. Rybakov, “Optimalnoe upravlenie stokhasticheskimi sistemami pri impulsnykh vozdeistviyakh, obrazuyuschikh erlangovskie potoki sobytii”, Programmnye sistemy: teoriya i prilozheniya, 4:2 (2013), 3–20  mathnet
    50. S. Ya. Serovaǐskiǐ, “Approximation Methods in Optimal Control Problems for Nonlinear Infinite-Dimensional Systems”, Math. Notes, 94:4 (2013), 567–582  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    51. S. Amat, I.K. Argyros, S. Busquier, R. Castro, S. Hilout, “Newton-type methods on Riemannian manifolds under Kantorovich-type conditions”, Applied Mathematics and Computation, 227 (2014), 762  crossref
    52. S. Amat, I. K. Argyros, S. Busquier, R. Castro, S. Hilout, “Traub-type high order iterative procedures on Riemannian manifolds”, SeMA, 63:1 (2014), 27  crossref
    53. Bogachev V., Smolyanov O., “Topological Vector Spaces and Their Applications”, Topological Vector Spaces and Their Applications, Springer Monographs in Mathematics, Springer, 2017, 1–456  crossref  isi
    54. A. V. Panteleev, K. A. Rybakov, “Optimal continuous stochastic control systems with incomplete feedback: approximate synthesis”, Autom. Remote Control, 79:1 (2018), 103–116  mathnet  crossref  isi  elib
  • Успехи математических наук Russian Mathematical Surveys
    Number of views:
    This page:1304
    Full text:550
    References:39
    First page:2

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019