Scientific Notes of

Taurida National V.I. Vernadsky University

Taurida National V.I. Vernadsky University

Series

Physical and Mathematical Sciences

**Vol. 19 (58), No. 1. 2006
****Mathematics.**** **

**Karpenko I.I, Sukhtaev
A.I., Tyshkevich D.L.**

Spectral
Decomposition of a Normal Operator in a Quaternionic
Hilbert Bimodule

*Using the new approach to the definition
of quaternionic analytic functions we received the
analogue of Cauchy's formulae. The theorem about
the partition of a quaternionic Hilbert bimodule
into the direct sum of the invariant submodules
for the continuous linear operator is proved, and
also the spectral decomposition of a normal (bounded)
operator in a quaternionic bimodule is constructed.*

**Lukjanova E.A., Mosentsova A.B.**

About
Solution's of Some Classes Integral Equation Best
Accuracy

*There is some method of approximated solution
of Fredgolm's equations of 2 class with kernel from
Sobolev's сlasses described in this article. Proposed
method consists in substitution kernel for its special
Furje's sum with numbers harmonyk choosed in special
way. There was proved that this method have the
best precision among all methods with fixing informational
vector's length.*

**Rudnitskiy O.I., Romanenko I.A.**

About
the Special Invariants of the Tetrahedral Groups,
Generated by Reflections on the Unitary Plane

*Let. PG be algebra, generated by Pogorelov
polynomials of the finite unitary reflection group
G. The degrees of generators of the algebra PG are
found in the case when G is the tetrahedral group,
generated by reflections on the unitary plane.*

**Starkov P.A.**

Interior
Problem for Stocks Equation

*An interior problem for linear hydrodynamics
equation is studied (the Stocks equations). Before
this the problem was not investigated. By the methods
of orthogonal projectors and auxiliary problems
a problem is taken to the abstract operator pencil
which was researched in previous author's works.*

**Tsvetkov D.O.**

About
One Initial Boundary Value Problem, Contected with
Motions of System Stratifieds Fluids

*There was investigated the problem on small
motions. The theorem on strong solvability of initial
boundary value; problem is proved.
*