Volume 3, Issue 5

The Gauss–Manin systems with coefficients having logarithmic poles along the discriminant sets of the principal deformations of complete intersection quasihomogeneous singularities S μ are calculated. Their solutions in the form of generalized hypergeometric functions are presented.

A strong type two-weight problem is solved for fractional maximal functions defined in homogeneous type general spaces. A similar problem is also solved for one-sided fractional maximal functions.

The problem we are dealing with consists in the following: find the necessary and sufficient conditions for the zero measure subset of the circumference at which points the bounded analytic function has no radial limits.

The estimate for the rate of convergence of approximate projective methods with one iteration is established for one class of singular integral equations. The Bubnov–Galerkin and collocation methods are investigated.

The conditions ensuring the correctness of the Cauchy problem on the nonnegative half-axis R + are found, where P : R + → R n × n and q : R + → R n are locally summable matrix and vector functions, respectively, t 0 ∈ R + and c 0 ∈ R n .

Entire modular forms of weights and for the congruence group Γ 0 (4 N ) are constructed, which will be useful for revealing the arithmetical sense of additional terms in formulas for the number of representations of positive integers by quadratic forms in 7 and 9 variables.