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TMF, 1984, Volume 59, Number 1, Pages 3–27 (Mi tmf4701)  

This article is cited in 49 scientific papers (total in 51 papers)

Differential calculus

V. S. Vladimirov, I. V. Volovich

Abstract: A new approach to superanalysis is developed on the basis of the theory of functions in Banach spaces and the theory of Banach algebras. In the framework of this superanalysis, an exposition is given of differential calculus.

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English version:
Theoretical and Mathematical Physics, 1984, 59:1, 317–335

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Received: 10.08.1983

Citation: V. S. Vladimirov, I. V. Volovich, “Differential calculus”, TMF, 59:1 (1984), 3–27; Theoret. and Math. Phys., 59:1 (1984), 317–335

Citation in format AMSBIB
\by V.~S.~Vladimirov, I.~V.~Volovich
\paper Differential calculus
\jour TMF
\yr 1984
\vol 59
\issue 1
\pages 3--27
\jour Theoret. and Math. Phys.
\yr 1984
\vol 59
\issue 1
\pages 317--335

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    This publication is cited in the following articles:
    1. V. S. Vladimirov, I. V. Volovich, “Superanalysis. II. Integral calculus”, Theoret. and Math. Phys., 60:2 (1984), 743–765  mathnet  crossref  mathscinet  zmath  isi
    2. I. V. Volovich, “Supersymmetric chiral field with anomaly and its integrability”, Theoret. and Math. Phys., 63:2 (1985), 533–535  mathnet  crossref  mathscinet  isi
    3. V. S. Vladimirov, I. V. Volovich, “Local and nonlocal currents for nonlinear equations”, Theoret. and Math. Phys., 62:1 (1985), 1–20  mathnet  crossref  mathscinet  zmath  isi
    4. V. S. Vladimirov, I. V. Volovich, “Conservation laws for non-linear equations”, Russian Math. Surveys, 40:4 (1985), 13–24  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. I. Ya. Aref'eva, I. V. Volovich, “Covariant quantization of gauge-invariant string field theories”, Theoret. and Math. Phys., 67:2 (1986), 521–524  mathnet  crossref  mathscinet  isi
    6. A. Yu. Khrennikov, “Second quantization and pseudodifferential operators”, Theoret. and Math. Phys., 66:3 (1986), 223–230  mathnet  crossref  mathscinet  zmath  isi
    7. A. Yu. Khrennikov, “Infinite-dimensional pseudodifferential operators”, Math. USSR-Izv., 31:3 (1988), 575–601  mathnet  crossref  mathscinet  zmath
    8. A. Yu. Khrennikov, “Superanalysis: Theory of generalized functions and pseudodifferential operators”, Theoret. and Math. Phys., 73:3 (1987), 1313–1320  mathnet  crossref  mathscinet  zmath  isi
    9. I. V. Volovich, “$p$-adic space-time and string theory”, Theoret. and Math. Phys., 71:3 (1987), 574–576  mathnet  crossref  mathscinet  zmath  isi
    10. A. Yu. Khrennikov, “Functional superanalysis”, Russian Math. Surveys, 43:2 (1988), 103–137  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    11. V. S. Vladimirov, “Generalized functions over the field of $p$-adic numbers”, Russian Math. Surveys, 43:5 (1988), 19–64  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    12. V. M. Buchstaber, A. N. Kholodov, “Groups of formal diffeomorphisms of the superline, generating functions for sequences of polynomials, and functional equations”, Math. USSR-Izv., 35:2 (1990), 277–305  mathnet  crossref  mathscinet  zmath
    13. A. Yu. Khrennikov, “The correspondence principle in quantum field theory and relativistic boson string theory”, Math. USSR-Sb., 67:1 (1990), 209–233  mathnet  crossref  mathscinet  isi
    14. A. Yu. Khrennikov, “Quantization of bosonic string field and infinite-dimensional pseudodifferential operators. Fixed gauge”, Theoret. and Math. Phys., 80:2 (1989), 829–838  mathnet  crossref  mathscinet  isi
    15. É. Yu. Lerner, M. D. Missarov, “Scalar models of $p$-adic quantum field theory and hierarchical models”, Theoret. and Math. Phys., 78:2 (1989), 177–184  mathnet  crossref  mathscinet  isi
    16. V. D. Ivashchuk, “Annihilators in infinite-dimensional Grassmann–Banach algebras”, Theoret. and Math. Phys., 79:1 (1989), 361–368  mathnet  crossref  mathscinet  zmath  isi
    17. A. Yu. Khrennikov, “Equatios on a superspace”, Math. USSR-Izv., 36:3 (1991), 597–627  mathnet  crossref  mathscinet  zmath  adsnasa
    18. A. Yu. Khrennikov, “Mathematical methods of non-Archimedean physics”, Russian Math. Surveys, 45:4 (1990), 87–125  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    19. A. Yu. Khrennikov, “Quantum mechanics over non-Archimedean number fields”, Theoret. and Math. Phys., 83:3 (1990), 623–632  mathnet  crossref  mathscinet  zmath  isi
    20. V. D. Ivashchuk, “Invertibility of elements in infinite-dimensional Grassmann–Banach algebras”, Theoret. and Math. Phys., 84:1 (1990), 682–688  mathnet  crossref  mathscinet  zmath  isi
    21. A. Yu. Khrennikov, “Generalized functions on a Non-Archimedean superspace”, Math. USSR-Izv., 39:3 (1992), 1209–1238  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    22. 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
    23. A. Yu. Khrennikov, “Real non-Archimedean structure of spacetime”, Theoret. and Math. Phys., 86:2 (1991), 121–130  mathnet  crossref  mathscinet  zmath  isi
    24. S. A. Duplij, “Types of $N=2$ superconformal transformations”, Theoret. and Math. Phys., 86:2 (1991), 138–143  mathnet  crossref  mathscinet  isi
    25. A. Yu. Khrennikov, M. Endo, “Unboundedness of a $p$-adic Gaussian distribution”, Russian Acad. Sci. Izv. Math., 41:2 (1993), 367–375  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    26. A. Yu. Khrennikov, “On the theory of infinite-dimensional superspace: reflexive Banach supermodules”, Russian Acad. Sci. Sb. Math., 77:2 (1994), 331–350  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    27. A. Yu. Khrennikov, “The infinite-dimensional Liouville equation”, Russian Acad. Sci. Sb. Math., 75:1 (1993), 17–41  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    28. V. D. Ivashchuk, “Tensor Banach algebras of projective type. I”, Theoret. and Math. Phys., 91:1 (1992), 336–345  mathnet  crossref  mathscinet  zmath  isi
    29. B. M. Zupnik, “Minimum deformations of commutative algebra and linear group $GL(n)$”, Theoret. and Math. Phys., 95:3 (1993), 677–685  mathnet  crossref  mathscinet  zmath  isi
    30. A. Yu. Khrennikov, R. Cianci, “Nonlinear evolution equations with (1,1)-supersymmetric time”, Theoret. and Math. Phys., 97:2 (1993), 1267–1272  mathnet  crossref  mathscinet  zmath  isi
    31. A. Yu. Khrennikov, “$p$-Adic probability theory and its applications. The principle of statistical stabilization of frequencies”, Theoret. and Math. Phys., 97:3 (1993), 1340–1348  mathnet  crossref  mathscinet  zmath  isi
    32. G. I. Kurapin, “On the existence and the stability of the solutions of certain nonlinear equations in topological modules of mappings”, Math. Notes, 54:1 (1993), 764–766  mathnet  crossref  mathscinet  zmath  isi  elib
    33. A. A. Gonchar, G. I. Marchuk, S. P. Novikov, “Vasilii Sergeevich Vladimirov (on his seventieth birthday)”, Russian Math. Surveys, 48:1 (1993), 201–212  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    34. A. Yu. Khrennikov, “Noncommutative analog of functional superanalysis”, Theoret. and Math. Phys., 103:2 (1995), 525–534  mathnet  crossref  mathscinet  zmath  isi
    35. S. A. Duplij, “The ideal structure of superconformal semigroups”, Theoret. and Math. Phys., 106:3 (1996), 291–306  mathnet  crossref  crossref  mathscinet  zmath  isi
    36. O. E. Galkin, “Infinite-dimensional superanalogs of the Mehler formula”, Math. Notes, 59:6 (1996), 671–675  mathnet  crossref  crossref  mathscinet  zmath  isi
    37. Duplij, S, “On supermatrix idempotent operator semigroups”, Linear Algebra and Its Applications, 360 (2003), 59  crossref  isi
    38. M. K. Kerimov, “Vasiliĭ Sergeevich Vladimirov (on the occasion of his eightieth birthday)”, Comput. Math. Math. Phys., 43:11 (2003), 1541–1549  mathnet  mathscinet
    39. M. D. Missarov, “Symmetry of the Renormalization Group in $p$-Adic Models”, Proc. Steklov Inst. Math., 245 (2004), 160–168  mathnet  mathscinet  zmath
    40. Proc. Steklov Inst. Math., 265 (2009), 30–58  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    41. E. N. Sattorov, “Reconstruction of solutions to a generalized Moisil–Teodorescu system in a spatial domain from their values on a part of the boundary”, Russian Math. (Iz. VUZ), 55:1 (2011), 62–73  mathnet  crossref  mathscinet  elib
    42. Y. C. Hon, Engui Fan, “Super quasiperiodic wave solutions and asymptotic analysis for $\mathcal N=1$ supersymmetric $KdV$-type equations”, Theoret. and Math. Phys., 166:3 (2011), 317–336  mathnet  crossref  crossref  adsnasa  isi
    43. Katanaev M.O., “Adiabaticheskaya teorema dlya konechnomernykh kvantovo-mekhanicheskikh sistem”, Izvestiya vysshikh uchebnykh zavedenii. Fizika, 54:3 (2011), 72–81  elib
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    45. Shou-fu Tian, Hong-qing Zhang, “Super Riemann theta function periodic wave solutions and rational characteristics for a supersymmetric KdV–Burgers equation”, Theoret. and Math. Phys., 170:3 (2012), 287–314  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    46. Petrov N.N., “O kantorovykh kubakh”, Vestnik sankt-peterburgskogo universiteta. seriya 1: matematika. mekhanika. astronomiya, 2012, no. 3, 53–58  elib
    47. M. D. Missarov, “Functional Fourier transformation and renormalization group transformation in bosonic field theory models”, Theoret. and Math. Phys., 174:2 (2013), 263–272  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    48. A. Yu. Khrennikov, B. Nilsson, S. Nordebo, “Quantum rule for detection probability from Brownian motion in the space of classical fields”, Theoret. and Math. Phys., 174:2 (2013), 298–306  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    49. D. S. Shirokov, “Pauli theorem in the description of $n$-dimensional spinors in the Clifford algebra formalism”, Theoret. and Math. Phys., 175:1 (2013), 454–474  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    50. S. V. Kozyrev, A. Yu. Khrennikov, V. M. Shelkovich, “$p$-Adic wavelets and their applications”, Proc. Steklov Inst. Math., 285 (2014), 157–196  mathnet  crossref  crossref  isi  elib  elib
    51. I. Ya. Aref'eva, I. V. Volovich, “Notes on the SYK model in real time”, Theoret. and Math. Phys., 197:2 (2018), 1650–1662  mathnet  crossref  crossref  adsnasa  isi  elib
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