An explicit kernel-split panel-based Nystr\"om scheme for integral equations on axially symmetric surfaces [PDF]
, 2016 A high-order accurate, explicit kernel-split, panel-based, Fourier-Nystr\"om discretization scheme is developed for integral equations associated with the Helmholtz equation in axially symmetric domains.
Helsing, Johan, Karlsson, Anders
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TO THE QUESTION OF UNIQUENESS OF DEGENERATE SINGULAR INTEGRAL EQUATIONS SOLUTIONS
Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2020 Background. The work is devoted to the study of sets of functions in which the condition for the unique solvability of degenerate singular integral equations is satisfied.
I. V. Boykov +2 more
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$L_{p;r} $ spaces: Cauchy Singular Integral, Hardy Classes and Riemann-Hilbert Problem in this Framework [PDF]
Sahand Communications in Mathematical Analysis, 2019 In the present work the space $L_{p;r} $ which is continuously embedded into $L_{p} $ is introduced. The corresponding Hardy spaces of analytic functions are defined as well. Some properties of the functions from these spaces are studied.
Ali Huseynli, Asmar Mirzabalayeva
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Gauge-Invariant Operators for Singular Knots in Chern-Simons Gauge Theory [PDF]
, 1997 We construct gauge invariant operators for singular knots in the context of Chern-Simons gauge theory. These new operators provide polynomial invariants and Vassiliev invariants for singular knots.
Akutsu +57 more
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Solutions of singular integral equations
International Journal of Mathematics and Mathematical Sciences, 1982 Qualitative behavior of solutions of possibly singluar integral equations is studied. It includes properties such as positivity, boundedness and monotonicity of the solutions of the infinite interval.
Rina Ling
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Boundedness for a Class of Singular Integral Operators on Both Classical and Product Hardy Spaces
Abstract and Applied Analysis, 2014 We found that the classical Calderón-Zygmund singular integral operators are bounded on both the classical Hardy spaces and the product Hardy spaces. The purpose of this paper is to extend this result to a more general class. More precisely, we introduce
Chaoqiang Tan
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Cosmological Perturbations from the No Boundary Euclidean Path Integral [PDF]
, 1999 We compute, from first principles, the quantum fluctuations about instanton saddle points of the Euclidean path integral for Einstein gravity coupled to a scalar field.
A. Linde +25 more
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A Regularization of Fredholm type singular integral equations
International Journal of Mathematics and Mathematical Sciences, 2001 We present a method to regularize first and second kind integral equations of Fredholm type with singular kernel. By appropriate application of the Poincaré-Bertrand formula we change such integral equations into a second kind Fredholm's integral ...
N. Aliev, S. Mohammad Hosseini
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On an Integral Equation with the Riemann Function Kernel
Axioms, 2022 This paper is concerned with a study of a special integral equation. This integral equation arises in many applied problems, including transmutation theory, inverse scattering problems, the solution of singular Sturm–Liouville and Shrödinger equations ...
Sergei Sitnik, Abdul Ahad Arian
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Approximate methods for solving degenerate singular integral equations
Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2023 Background. Singular integral equations in degenerate cases describe many processes in natural science and technology. The theory of these equations has been studied quite well, but as far as the authors know, there are currently no analytical methods ...
Il'ya V. Boykov, Anastasiya A. Pivkina
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