Speciality:
01.01.03 (Mathematical physics)
Birth date:
9.01.1923
Keywords: equations and models of mathematical physics; generalized functions; functions of several complex variables;manydimentional tauberian theory; p-adic analysis; number theory; numerical methods; quantum field theory.
Subject:
The first example of the form extreme and not perfect (with 6 variables) was constructed (the Voronoi hypothesis was confirmed). The boundary value problem for the transfer equation was investigated: correctness, new variational priciple, boundary conditions in the spherical harmonic method, singularity of solutions. A method for numerical solution of transfer equation for a multilayer ball was created and its convergence and stability were proved. The factorization method for numerical solution of diffusion equation for a multilayer ball was proposed and its convergence and stability were proved. Applications of the Monte Carlo method for solution the transfer equation of neutrons and radiation was developed. The quadrature formula of the Simpson type for numerical calculations of the Wiener integrals was proposed and its convergence was proved. The "C-convex hull" theorem was proved and its applications to axiomatic quantum field theory were given: the proof of dispersion relations, the "finite covariance" theorem (with N. N. Bogolubov). In papers (with N. N. Bogolubov, A. N. Tavkhelidze and B. I. Zavialov) the theoretical explanation of automodel behavior of form-factors of deep inelastic processes of lepton-hadron scattering by high energies and great momentum transfer was given on the basis of Bogolubov's axiomatic. The algebra of tempered holomorphic functions in tube domains over cone (boudary behavior, integral representations, the Fourier-transform) was investigated and were given applications to many-dimesional cojugate problems for holomorphic functions, to indicatrix of grouth of plurisubharmonic functions, to holomorphic functions with positive real part. More detailed the special case of the future tube has been considered. The many-dimensional linear passive systems with respect to a causal cone were investigated. A number of papers (with Yu. N. Drojjinov and B. I. Zavialov) were devoted to many-dimensional tauberian theorems for generalized functions. In papers (with I. V. Volovich and V. V. Zharinov) was proposed the general method of constraction conservation laws (local or not) both for linear and for nonlinear integrodiffere ntial equations. In papers with I. V. Volovich two problems of statistical physics have been investigated: the Gaussian model on semi-axis with interaction defined by the Toeplitz matrixes, and antiferromagnetic Ising model in magnetic field. The connection with the theory of orthogo nal polynomials was established, new estimates of determinants of the Toeplitz matrixes were given. Jointly with I. V. Volovich superanalysis (differential and integral calculus) was constru cted on the basis of concept of point superspace, and some applications to the supersymmet ric Yang–Mills equation were given. The Riemann–Hilbert problem of linear conjugation in the Nevanlinna and Smirnov classes and the associated Wiener–Hopf equation in class of ultradistributions were posed and solved. The $p$-adic quantum machanics for the harmonic oscillator (with I. V. Volovich and E. I. Zelenov) was formulated and studied. The pseudodifferential operator of (fractional) differentiation and integration for comp lex-valued functions of $p$-adic arguments was defined and studied. The spectral theory of the $p$-adic pseudodifferential operators of the Schroedinger type was worked out. The regularized adelic formulas for the tree string and superstring amplitudes (beta-functions) in any algebraic number field were derived, in particular, more detailed formulas has been obtained in the field of rational numbers, and in the one-class quadratic fields. Jointly with G. I. Marchuk the determination of the adjoint operator for nonlinear problems was suggested, their properties were studied and some applications were given. The new beta-function for evaluation of the tree massless superstring amplitudes was introduced and studied.
Main publications:
Vladimirov V. S., “Chislennoe reshenie kineticheskogo uravneniya dlya shara”, Vychislitelnaya matematika, 3, 1958, 3–33
Vladimirov V. S., Volovich I. V., “Lokalnye i nelokalnye toki dlya nelineinykh uravnenii”, TMF, 62 (1985), 3–29
Vladimirov V. S., “On the Freund–Witten Adelic Formular for Veneziano Amplitudes”, Lett. Math. Phys., 27 (1993), 123–131
Vladimirov V. S., “Adelnye formuly dlya gamma- i beta-funktsii odnoklassnykh kvadratichnykh polei. Primeneniya k 4-chastichnym strunnym amplitudam”, Trudy Matem. in-ta im. V. A. Steklova, 228, 2000, 76–89
Vladimirov V. S., Uravneniya matematicheskoi fiziki, Izd. I–V, Nauka, M., 1967, 1971, 1976, 1981, 1983
