On this page you can
find short descriptions of some of my old papers. Most of the
interesting stuff was later included in the papers that are accessible
to English speaking readers.
1. A.G. Baskakov and IK.
On
the Spectral Properties of Causal Operators,Vestnik
VGU: Physics, Mathematics, No.
2, 2002, pdf
(Russian):
This short article announces some of the results that appeared later in
my Ph.D. thesis (Sect. 6-9, 11) and the paper
in Izvestiya RAN. With
the exception of the last theorem the above manuscripts cover the
material of the paper. This last theorem, in a way, asserts that the
"anti-memory" of the inverse of a causal operator "decays
exponentially". The proof (not presented in the paper) uses
methods of abstract holomorphic functions. The Tübinger
Berichte preprint
is a slightly modified translation of this paper.
Vestnik
VGU is a peer-reviewed periodic journal published by Voronezh State
University (VGU). It is intended for promotion of the results by local
researchers.
2. IK. On invertibility criteria in
the
algebra of
causal operators,Vestnik
VGU: Physics, Mathematics, No.
1, 2002, pdf
(Russian):
This paper became the basis for Sect. 14 of my Ph.D. thesis. The main
theorem there comes with the longest proof I have come up with so far.
Some day I intend to publish a more general version of it.
3. IK.Invertibility and causal invertibilityof operators with
the
two-point Beurling spectrum,Izvestiya
Ross. Akad. Estestv. Nauk, Ser. MMMIU, 4 (4) 2000:
This paper became the basis for Sect. 13 of my
Ph.D. thesis. A different point of view on the same kind of
problems is
presented in the paper
in JMAA.
4. S.Yu.
Balasheva, IK,
I.A. Rodionova, and N.A.
Zhdankina. On a
problem of uniform
distribution of multiplying traffic flows,in
"System modelling of socio-economic processes", Voronezh, 2000
(Russian), pp. 47-51.
This little note that I wrote with my fellow classmates describes
a solution to a certain interesting optimisation problem. We came up
with it while attending a course in network flows.
The collection of papers it is included in was published to commemorate
the 30th anniversary of the sub-department of Voronezh university which
supervised my study and work while I was there.
5. IK and T.N.
Vinokurova. Preference
projection method
for a
neoclassic consumption model,in
"System modelling of socio-economic processes", Voronezh, 2000
(Russian), pp. 72-74.
This note was written with another classmate and describes a solution
to another optimasation problem. This problem was suggested to us when
we were attending a course in economic modelling.
6. I. F.
Astakhova, IK et
al. Employment
of Expert System Generator
“Expert-M” when working with economic models, Interuniversitary
Collection of
Articles “Russian Economy at Present”, Voronezh, 1998, pp. 18-28
(Russian).
7. I.
F. Astakhova and IK. Expert
System Generator
“Expert-M”, Student
manual, Voronezh, 1998, 20 pp. (Russian).
This manual explains to students how to work with the above piece of
software (utterly obsolete by now). It was written together with the
instructor of the course in Data Bases and Artificial Intelligence
while I was attending it. The above paper, published in a
collection of articles by several local universities, describes how
that piece of software could be used for a couple of economic models.
8. IK. On
C*-algebra generated by one or two idempotents,Vestnik
VGU: Physics, Mathematics, No. 3, 1998, pp. 238-242.
This is one of my first papers written as an undergraduate. There I
describe multiplicative homomorphisms of certain C*-algebras and obtain
some interesting ineqaulities involving norms of projections. I
believe, most of these results were known by then but accessing the
literature was (and still is) a problem in a provincial Russian
university.