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Published in 2019 at "Acta Mathematica Sinica, English Series"
DOI: 10.1007/s10114-019-8270-3
Abstract: In this paper, the weak (1,1) boundedness of oscillatory singular integral with variable phase P(x)γ(y) for any x, y ∈ ℝ, $$Tf(x)\;:=\;{\rm{p}}.\>{\rm{v}}.\>\int_{- \infty}^\infty {{{\rm{e}}^{{\rm{i}}P(x)\gamma (y)}}f(x\;-\;y)\frac{dy}{y}}$$ is studied, where P is a real monic polynomial on…
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Keywords:
variable phase;
integral variable;
weak boundedness;
singular integral ... See more keywords
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Published in 2020 at "Complex Analysis and Operator Theory"
DOI: 10.1007/s11785-021-01110-w
Abstract: Some basics of a theory of unbounded Wiener–Hopf operators (WH) are developed. The alternative is shown that the domain of a WH is either zero or dense. The symbols for non-trivial WH are determined explicitly…
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Keywords:
unbounded wiener;
hopf operators;
wiener hopf;
singular integral ... See more keywords
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Published in 2018 at "Engineering Analysis With Boundary Elements"
DOI: 10.1016/j.enganabound.2018.07.004
Abstract: Abstract In the paper singular integral equations for anisotropic plates with inclusions (the Dirichlet problem) are developed in the simple form on the basis of established dependencies between the Lekhnitskii complex potentials, stress and displacements.…
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Keywords:
singular integral;
anisotropic plates;
method;
stress ... See more keywords
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Published in 2019 at "Engineering Analysis with Boundary Elements"
DOI: 10.1016/j.enganabound.2019.03.039
Abstract: Abstract In this paper, the singular integral equations are written for anisotropic plates with elastic anisotropic inclusions in a simple form based on simple dependencies between the Lekhnitskii complex potentials and stress and strain [5]…
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Keywords:
determination stresses;
anisotropic plates;
integral equations;
singular integral ... See more keywords
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Published in 2017 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2017.01.052
Abstract: Abstract Let α and β be orientation-preserving diffeomorphism (shifts) of R + = ( 0 , ∞ ) onto itself with the only fixed points 0 and ∞. We establish a Fredholm criterion and calculate…
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Keywords:
integral operators;
weighted singular;
slowly oscillating;
singular integral ... See more keywords
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Published in 2018 at "Journal of Electromagnetic Waves and Applications"
DOI: 10.1080/09205071.2017.1383943
Abstract: Abstract The E- polarized plane wave diffraction by the infinite periodic grating with removed strip is considered. The scattered field is represented as a sum of the field of the infinite periodic grating and the…
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Keywords:
strip;
field;
infinite periodic;
diffraction ... See more keywords
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Published in 2020 at "Complex Variables and Elliptic Equations"
DOI: 10.1080/17476933.2020.1722113
Abstract: In this paper, we obtain conditions of Noetherian solvability and the Index formula for a singular integral equation with a Cauchy kernel and a Carleman shift in Besov space, which is embedded into the space…
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Keywords:
integral equation;
singular integral;
noetherian solvability;
carleman shift ... See more keywords
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Published in 2018 at "Differential Equations"
DOI: 10.1134/s0012266118090100
Abstract: Theorems providing the convergence of approximate solutions of linear operator equations to the solution of the original equation are proved. The obtained theorems are used to rigorously mathematically justify the possibility of numerical solution of…
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Keywords:
electromagnetism;
discretization methods;
methods three;
equations electromagnetism ... See more keywords
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Published in 2017 at "Mathematical Problems in Engineering"
DOI: 10.1155/2017/6148393
Abstract: We study singular integral equations of convolution type with cosecant kernels and periodic coefficients in class . Such equations are transformed into a discrete jump problem or a discrete system of linear algebraic equations by…
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Keywords:
cosecant kernels;
equations convolution;
type cosecant;
integral equations ... See more keywords
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Published in 2018 at "Journal of Function Spaces"
DOI: 10.1155/2018/1949747
Abstract: In this article, the higher integrability of commutators of Calderón-Zygmund singular integral operators on differential forms is derived. Also, the higher order Poincaré-type inequalities for the commutators acting on the solutions of Dirac-harmonic equations are…
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Keywords:
calder zygmund;
zygmund singular;
commutators calder;
integrability commutators ... See more keywords
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Published in 2020 at "Georgian Mathematical Journal"
DOI: 10.1515/gmj-2020-2082
Abstract: Abstract The paper deals with the three-dimensional Robin type boundary-value problem (BVP) for a second-order strongly elliptic system of partial differential equations in the divergence form with variable coefficients. The problem is studied by the…
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Keywords:
domain singular;
localized boundary;
boundary domain;
singular integral ... See more keywords