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Vol 53, No 4 (2018)
- Year: 2018
- Articles: 6
- URL: https://journals.rcsi.science/1068-3623/issue/view/14087
Functional Analysis
On Solvability of Regular Hypoelliptic Equations in ℝn
Abstract
In this paper the unique solvability of regular hypoelliptic equations in multianisotropic weighted functional spaces is proved by means of special integral representation of functions through a regular operator. The existence of the solutions is proved by constructing approximate solutions using multianisotropic integral operators.
187-200
Integral Equations
A One–parameter Family of Bounded Solutions for a System of Nonlinear Integral Equations on the Whole Line
Abstract
A system of nonlinear integral equations with a convolution type operator arising in the p–adic string theory for the scalar tachyons field is studied. The existence of a one–parameter family of monotone continuous and bounded solutions for this system is proved. The limits of the constructed solutions at ±∞ are calculated.
201-211
Real and Complex Analysis
On Dirichlet Type Spaces Aω2 Over the Half–Plane
Abstract
Some extensions of the results of the first author related with the Hilbert spaces Aω,02 of functions holomorphic in the half–plane are proved. Some new Hilbert spaces Aω2 of Dirichlet type are introduced, which are included in the Hardy space H2 over the half–plane. Several results on representations, boundary properties, isometry, interpolation, biorthogonal systems and bases are obtained for the spaces Aω2 ⊂ H2.
212-222
On Uniqueness of Series by General Franklin System
Abstract
The paper considers the general Franklin system corresponding to a regular by couples partition of the segment [0; 1]. For series by this system, we prove uniqueness theorems and obtain restoration formulas for coefficients, provided that the series converge in measure and satisfy some necessary condition.
223-231
Probability Theory and Mathematical Statistics
232-236
Method of Moments Estimators and Multi–step MLE for Poisson Processes
Abstract
We introduce two types of estimators of the finite–dimensional parameters in the case of observations of inhomogeneous Poisson processes. These are the estimators of the method of moments and Multi–step MLE. It is shown that the estimators of the method of moments are consistent and asymptotically normal and the Multi–step MLE are consistent and asymptotically efficient. The construction of Multi–step MLE–process is done in two steps. First we construct a consistent estimator by the observations on some learning interval and then this estimator is used for construction of One–step and Two–step MLEs. The main advantage of the proposed approach is its computational simplicity.
237-246