Results 261 to 270 of about 10,334 (309)
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2002
The celebrated Cauchy singular integral operator on a Jordan curve, or more precisely, its 1-periodic counterpart is perhaps the most important brick in the theory of periodic integral and pseudodifferential operators. In this chapter, we first treat the Cauchy singular operators in the Holder spaces C α (Γ) and after that we extend the results to L 2 ...
Jukka Saranen, Gennadi Vainikko
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The celebrated Cauchy singular integral operator on a Jordan curve, or more precisely, its 1-periodic counterpart is perhaps the most important brick in the theory of periodic integral and pseudodifferential operators. In this chapter, we first treat the Cauchy singular operators in the Holder spaces C α (Γ) and after that we extend the results to L 2 ...
Jukka Saranen, Gennadi Vainikko
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1989
In this chapter we will consider one-dimensional singular integral equations involving Cauchy principal values that arise from boundary value problems for holomorphic functions. The investigations of these integral equations with Cauchy kernels by Gakhov, Muskhelishvili, Vekua, and others have had a great impact on the further development of the ...
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In this chapter we will consider one-dimensional singular integral equations involving Cauchy principal values that arise from boundary value problems for holomorphic functions. The investigations of these integral equations with Cauchy kernels by Gakhov, Muskhelishvili, Vekua, and others have had a great impact on the further development of the ...
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1995
Let the function f be defined on I=[a,b] and, possibly, be singular at an interior point c∈(a,b). Recall that the improper integral was defined by $$\int\limits_{a}^{b} {f\left( x \right)} dx: = \mathop{{\lim }}\limits_{{\mathop{{{{\varepsilon }_{1}} \to 0}}\limits_{{{{\varepsilon }_{1}} > 0}} }} \int\limits_{a}^{{c - {{\varepsilon }_{1}}}} {f\left(
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Let the function f be defined on I=[a,b] and, possibly, be singular at an interior point c∈(a,b). Recall that the improper integral was defined by $$\int\limits_{a}^{b} {f\left( x \right)} dx: = \mathop{{\lim }}\limits_{{\mathop{{{{\varepsilon }_{1}} \to 0}}\limits_{{{{\varepsilon }_{1}} > 0}} }} \int\limits_{a}^{{c - {{\varepsilon }_{1}}}} {f\left(
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A Method for Studying Singular Integral Equations
Siberian Mathematical Journal, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Normalization of Systems of Singular Integral Equations
Differential Equations, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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2012
The theory introduced in previous chapters, especially the Fredholm Theory, was presented under the restrictive assumptions that the kernel was continuous on its domain of definition and that the interval of integration was finite. There is no guarantee that those results or similar ones will hold if the kernel has an infinite discontinuity or if the ...
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The theory introduced in previous chapters, especially the Fredholm Theory, was presented under the restrictive assumptions that the kernel was continuous on its domain of definition and that the interval of integration was finite. There is no guarantee that those results or similar ones will hold if the kernel has an infinite discontinuity or if the ...
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On Spline Collocation for Singular Integral Equations
Mathematische Nachrichten, 1983AbstractThis paper is devoted to the approximate solution of one‐dimensional singular integral equations on a closed curve by spline collocation methods. As the main result we give conditions which are sufficient and in special cases also necessary for the convergence in SOBOLEV norms.The paper is organized as follows.
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A Particular Class of Singular Integral Equations
SIAM Journal on Applied Mathematics, 1971The integral equation \[ \int_0^1 \left\{ \frac{1}{y - x} + \frac{{P_n [y/(y + x)]}}{{y + x}} \right\}\varphi (y) dy = h(x),\quad 0 < x < 1, \], with $P_n (z)$ representing a polynomial of degree n, is investigated. A change of variables $(x = \exp ( - t),y = \exp ( - t))$ transforms the equation into one of the Wiener-Hopf type.
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On Singular Normal Linear Integral Equations
Canadian Mathematical Bulletin, 1970In this work we consider the equation1where K(x, y) is singular in the sense that it does not properly belong to L2 and f(x) is an arbitrary L2 function.A Lebesgue measurable function K(x, y) of two variables, having real values on [0.1] × [0.1] is called a singular normal kernel ...
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