Let two bounded simply connected domains $D\subset {\mathbb C}_{z}$, $G\subset {\mathbb C}_{w}$, and two locally regular compact subsets $E\subset D,\, \, \, F\subset G$ be given. If $f(z,w)$ is a separately analytic function with finitely many singular points in each section of $D\times \left\{w^{0} \right\}$ and $\left\{z^{0} \right\}\times G$ for any $(z^{0} ,w^{0} )\in E\times F$ on the set $X=(D\times F)\cup (E\times G),$ then it extends holomorphically to the domain \[\hat{X}=\left\{(z,w)\in D\times G:\, \, \, \omega^{*}(z,E,D)+\omega^{*}(w,F,G)
| Mualliflar | Imomkulov, S., Rasulov, K. |
|---|---|
| Jurnal | O‘zbekiston matematika jurnali |
| Nashr sanasi | 2026-03-25 |
| Jild | 70 |
| Son | 1 |
| Til | Ingliz |
| DOI | 10.29229/uzmj.2026-1-9 |
DOI: 10.29229/uzmj.2026-1-9 · Maqolaning asl sahifasi
Hartogs's phenomena, separately analytic functions, harmonic measure, singular set
We consider a model of one-dimensional Schr\"odinger Hamiltonian perturbed by two identical non-local interactions of the form $\delta'(x\pm y)$, symmetrically located at the points $ \pm y$ from the origin. The…
In this paper, we aim to study the Cauchy problem posed for a fractional order equation. General solution of the time-fractional equation is found by the Fourier method. The solution to the given problem is shown to be…
We consider the Hamiltonian of a system of two fermions on a two-dimensional lattice ${\mathbb{Z}}^2$ with a certain type potential. It is proved that the subspace of odd functions $L^o_{ {2}} {(}{\mathbb{T}}^{ {2}}…
This article addresses the well-posedness of a coefficient inverse problem for the three-dimensional Tricomi equation in a parallelepiped. For this problem with nonlocal boundary conditions in anisotropic Sobolev…
This work focuses on classifying three-dimensional complex Leibniz dialgebras. We present a complete list of these algebras when the annihilator of the associated Leibniz algebra is one-dimensional.
In the article, high-accuracy difference schemes for the Cauchy problem for a system of fourth-order equations are obtained. Based on the method of energy inequalities, the stability of the scheme is proved, a priori…
Non-homogeneous Beatty sequence is a sequence of positive integer that taking the floor value of irrational numbers. This paper using the prime counting function, $\pi(x)$ to estimate the cardinality of total distinct…
The paper considers a mixed problem for a quasilinear system of hyperbolic equations in Riemann invariants with dissipative nonlinear boundary conditions. To numerically solve the mixed problem, an initial-boundary…
This paper investigates the influence of the symmetric product functor $SP^{n}$ and the exponential functor $\exp$ on certain types of continuous mappings, focusing specifically on almost-open and pseudo-open mappings…
In this paper, a new family of Pauli quaternions whose components are the Gaussian Leonardo numbers is defined. These new Pauli quaternions are called Pauli Gaussian Leonardo quaternions. Furthermore, several properties…