SCIENTIFIC ABSTRACT FADEYEV, L.D. - FADDEYEVA, V.K.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000412320019-9
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: January 3, 2017
• Document Release Date: July 28, 2000
• Sequence Number: 19
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

AUTHORs Mayevo Lo' D. 20-5-8/54
TITLE: on an Expression for the Trace of the Difference of Two Singular
Differential Operators of the Sturm-Liouville's Type (0 vyrazhenii
dlya sled& rasnosti dvukh singulyarnykh differaixtsiallnykh
operatorov tipa. Shturma-Liu-villya)
PERIODICALs Doklady Akad.Nauk SSSR 1957,Vol.115,Nr-5, pp-878-881 (USSR)
ABSTRAM The f arnala.1 or the traza.-of the. dif f errence of. two- regular
3 turn- Liouvil le ',~..oporators with & -discrete. spacrt-rum-found by
Ge2fand and Lovitan,[Ref.17 is extended. by the author in the
simplest special case to operators with a continuous spectrum. The
operators L Y -Y lf+q,(x)y, y(0) - 0, 1-1,2, are considered.
Theorem: If 1) 10 do xlq,(x)ldx4.oo , 1-1,2, 2) g(x)-ql(x)-q,(x)
is continuous in the neighborhood of x - 0 and 3) Tfr(x)dx - 0,
0
then the trace of L 1_L2 is finite and there holds the formula
Card 1/2 Sp (L -L?) - --I (ql(o)-q
1 4

20-5-8/54
On an Expression for the Trace of the Difference of Tdo Singular
Differential Operators of the Sturm-Liouville's 7~jx (cont - )
ASSOCIATION- leningrad State University lm. A. A. Zbdanoy (leningradskiy gosudar-
stveunyy universitet im. A. A. Zhdanova)
PMSERMD: W V. I. Smirmov, Ac&lemician, Wrch 1, 1957
SUBMITZD: Ftbrwry 20,, 1957
AVAILABLE: Library of Congress
Card 2/2

LADYZHENSKAYAj 0. A. and FADDMV, L. D.
"Perturbation Theory of a Continuous Spectrum."
paper submitted at International Congress Mathematicians, Edinburgh, 14 - 21 Aug
1958.

24 (5)
AUTHOR: Faddeyev, L. D.
SOV/56-35-2-17/60
TITLE: On the Dispersion Relations in the Nonrelativistic
Scattering Theory (0 dispersionnykh sootnosheniyakh v
nerelyativistskoy teorii rasseyaniya)
PERIODICAL: Zhurnal eksperimentallnoy i teoreticheskoy fiziki, 1958,
Vol 35, Nr 2, pp 433-439 (USSR)
ABSTRACT: The present paper is a continuation of several papers:
(Wong, Khuri, Van Kampen, Jostand Pais, references 1 - 4t
- investigation of dispersion conditions with S-matrix at
complex energies - with special causality principle
- according to the theory developed by Fredholm (Fredgollm)),.
In the present paper the author suggests a relatively simple
derivation of dispersion conditions, in which the problem
is reduced to an investigation of the properties of Green's
(Grin) function of the total Hamiltonian. Derivation is of
a general character and is suited for any amplitudes of
scattering on a potential. The author demonstrates this
method on the basis of the problem of scattering on a
Card 1/2 fixed three-dimensional center (nonrelativiatic ansatz)-.

On the Dispersion Relatims in the Nonrelativistic SOV/56-35-2-17/60
Scattering Theory
In this way it is possible to verify the results obtained
by Wong and Khuri. In the last chapter of the paper the
connection between the dispersion relations and the problems
relating to the complete characteristic of the S-matrix,
(by means of the K-matrix 3 - (1 + iK)(1 - iK)-') for
04E