Description of older papers/preprints

 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 invertibility of 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.