Weak (1,1) Boundedness of Oscillatory Singular Integral with Variable Phase
Sign Up to like & getrecommendations! 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… read more here.
Keywords: variable phase; integral variable; weak boundedness; singular integral ... See more keywords
Unbounded Wiener–Hopf Operators and Isomorphic Singular Integral Operators
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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… read more here.
Keywords: unbounded wiener; hopf operators; wiener hopf; singular integral ... See more keywords
Determination of stress state of anisotropic plates with rigid inclusions based on singular integral equations
Sign Up to like & getrecommendations! 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.… read more here.
Keywords: singular integral; anisotropic plates; method; stress ... See more keywords
Determination of stresses in anisotropic plates with elastic inclusions based on singular integral equations
Sign Up to like & getrecommendations! 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]… read more here.
Keywords: determination stresses; anisotropic plates; integral equations; singular integral ... See more keywords
The index of weighted singular integral operators with shifts and slowly oscillating data
Sign Up to like & getrecommendations! 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… read more here.
Keywords: integral operators; weighted singular; slowly oscillating; singular integral ... See more keywords
Singular integral equations in diffraction problem by an infinite periodic strip grating with one strip removed: E–polarization case
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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… read more here.
Keywords: strip; field; infinite periodic; diffraction ... See more keywords
Noetherian solvability of an operator singular integral equation with a Carleman shift in fractional spaces
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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… read more here.
Keywords: integral equation; singular integral; noetherian solvability; carleman shift ... See more keywords
Discretization Methods for Three-Dimensional Singular Integral Equations of Electromagnetism
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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… read more here.
Keywords: electromagnetism; discretization methods; methods three; equations electromagnetism ... See more keywords
Singular Integral Equations of Convolution Type with Cosecant Kernels and Periodic Coefficients
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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… read more here.
Keywords: cosecant kernels; equations convolution; type cosecant; integral equations ... See more keywords
The Higher Integrability of Commutators of Calderón-Zygmund Singular Integral Operators on Differential Forms
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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… read more here.
Keywords: calder zygmund; zygmund singular; commutators calder; integrability commutators ... See more keywords
Localized boundary-domain singular integral equations of the Robin type problem for self-adjoint second-order strongly elliptic PDE systems
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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… read more here.
Keywords: domain singular; localized boundary; boundary domain; singular integral ... See more keywords