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1957, Volume 12, Issue 1(73)  


Computation of the amount of information about a stochastic function contained in another such function
I. M. Gel'fand, A. M. Yaglom
3
Variational problems with admissible surfaces of arbitrary topological types
A. G. Sigalov
53
On the theorem of uniform continuity
V. A. Uspenskii
99

Scientific communications
Reconstruction of the potential energy from the scattering matrix
Z. S. Agranovich, V. A. Marchenko
143
A class of generalized functions
V. M. Babich
145
Differential geometry of smooth manifolds
I. Ya. Bakelman
145
Eigenfunction expansions of general self-adjoint differential operators
Yu. M. Berezanskii
147
On an inverse problem of spectral analysis for the Schrödinger equation
Yu. M. Berezanskii
147
Hypercomplex systems with continual basis
Yu. M. Berezanskii, S. G. Krein
147
Laplace operators on semisimple Lie groups and on certain symmetric spaces
F. A. Berezin
152
Constructing of variational methods for elliptic differential equations
M. Sh. Birman
157
On critical values of certain functionals in Banach spaces
Yu. G. Borisovich
157
On a possible generalization of the method of orthogonal trajectories
M. A. Krasnosel'skii
160
Certain questions of functional analysis and variational methods of investigation of non-linear equations
M. M. Vainberg
162
On certain methods of approximate solutions of non-linear functional equations in Banach spaces
B. A. Vertgeim
166
Application of the theory of partially ordered spaces to the study of self-adjoint operators in Hilbert space
B. Z. Vulikh
169
Approximate determination of eigenvalues and the theory of perturbation
M. K. Gavurin
173
Difference method of computation of shock waves
S. K. Godunov
176
On the index, null elements and elements of the kernel of an unbounded operator
I. Ts. Gokhberg
177
Unitary representations of real simple Lie groups
M. I. Graev
179
Integration and differentiation of functions of Hermitian operators depending on a parameter
Yu. L. Daletskii
182
On approximation of abstract functions
S. I. Zukhovitskii, S. B. Stechkin
187
On convergence of sequences of functions in certain functional spaces
V. P. Il'in
192
On approximate solution of non-linear operator equations by iterative methods
Yu. Ya. Kaazik
195
On linear and bilinear transformation of sequences in Banach space
G. F. Kangro
199
Harmonic analysis of fast growing functions
B. I. Korenblum
201
Generalized solutions of elliptic differential equations and their summability in $L_p$
A. I. Koshelev
203
Study of the spectrum of a nonlinear operator in the neighborhood of a point of bifurcation and applications to the problem of longitudinal bending of a compressed rod
M. A. Krasnosel'skii
203
Differential equations in a Banach space and their application in hydromechanics
S. G. Krein
208
On non-linear equations with positive non-linearities
L. A. Ladyzhenskii
211
The method of non-selfadjoint operators in scattering theory
M. S. Livshits
212
Some problems of the spectral theory of systems of differential equations
V. B. Lidskii
218
Existence of fundamental solution of equations of elliptic type
Yu. I. Lyubich
218
The principle of St. Venant and oscillating functions
S. I. Mel'nik
218
Some theorems of non-linear functional analysis and their application in the theory of local groups
D. P. Mil'man
222
Completeness of the system of eigenfunctions and associated functions of elliptic differential operators
B. M. Naimark
226
A lattice characterization of function spaces
A. G. Pinsker
226
Expansions in functions that are solutions of scattering problem
A. Ya. Povzner
230
Bundles of hyperplanes in linear spaces
D. A. Raikov
230
On a class of Banach spaces
Ya. B. Rutitskii
230
Operator equations in partially ordered spaces and some qualitative theorems for linear partial differential equations
M. A. Rutman
234
Investigation of the rapidity of convergence of the method of quickest descent
B. A. Samokish
238
Construction of operators of transformation and solution of a problem of moments for ordinary linear differential equations of arbitrary order
M. K. Fage
240
On the well-posedness and convergence of difference equations
A. F. Filippov
245
On a new problem of theoty of trans-sonic flows
F. I. Frankl'
245
On certain problems of the general theory of commutative normed rings
G. E. Shilov
246
On subrings of the ring of continuous functions
I. M. Gel'fand
249
Generalized resolvents of symmetric operators and eigenfunction expansions of a class of boundary problems
A. V. Strauss
251
On regular and parabolic systems of partial differential equations
S. D. Èidel'man
254
Variational problems with retarded argument
L. È. Èl'sgol'ts
257

Letters to the Editor
Letter to the Editor
K. A. Bagrinovskii
259
Erratum
R. N. Shcherbakov
259
Erratum
P. G. Kontorovich
261
Correction
262
Erratum
A. A. Gol'dberg
262
Erratum
M. F. Shirokhov
262
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