Mathematics |
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2004, No. 2
Y.S. Baburin
In the paper inversion formulas of the normal cases for three variants of the complete singular integral equation of the second kind with Caushy's kernel (that is the complete SIE-2C) and an unclosed contour of integration are given in the analytic form. It is show that due to the specific substitution of the variables in the singular integral that uses group's properties of the kernel and reduces the complete SIE-2C to the normal case of the characteristic type of the SIE-2C on any finite or semi-infinite contour of integration.
R.P. Uzbekov
INTERPOLATION BETWEEN R. I. SPACE X AND Lp, 1 < p < ∞
This paper is devoted to problems of the interpolation theory of weak type operators. The conditions for rearrangement invariant (r.i.) function space X on [0,1], having the property: if Y - r.i. space on [0,1] and Y is the interpolation space between X and L∞, α(Y)>p-1 (1 < p < ∞ ) (the Boyd index) then Y is the interpolation space between X and Lp, are given. It is shown that the Lorentz spaces Lq,r , 1 ≤ r < p < ∞ , 1 ≤ q ≤ ∞ have such a property.
O.P. Filatov
ON THE EULER METHOD FOR THE CARATHEODORY DIFFERENTIAL EQUATIONS
In the paper the accuracy of the approximate solutions of the Caratheodory differential equations with a given initial value by the Euler integral discretization scheme is estimated.
Ch.A. Chikhanov
THE ELLIPTIC JACOBI FUNCTIONS AND THEIR GENERALIZATIONS IN THE CASE OF ARBITRARY PERIODS
In the paper a new class of elliptic functions (generalizing the classical Jacobi functions) is introduced. Relations for generalized elliptic functions analogues those valid for Jacobi's functions are obtained.