We consider the first-kind Fredholm integral equatlon (A upsilon)(x) = f(x), x is an element of R+, where A is the Stieltjes transform defined as [GRAPHICS] Under some regularity assumptions on f we prove that the above problem is well-posed according to Tikhonov; that is, for any f in a given class of data there exists a unique solution upsilon of the above equation, and if \f(x)\ less than or equal to epsilon, For All x is an element of R+, for some positive is an element of then \v(y)\ less than or equal to alpha(epsilon), For All y is an element of [a, b], where alpha(epsilon) is a continuous non-decreasing function with alpha(0) = 0. An expression of the solution upsilon by means of a convergent Fourier series is also given.

First-kind Fredholm integral equations with kernel of Hankel type / A., Losi; Sacchetti, Andrea. - In: INVERSE PROBLEMS. - ISSN 0266-5611. - STAMPA. - 15(1999), pp. 281-290.

First-kind Fredholm integral equations with kernel of Hankel type

SACCHETTI, Andrea
1999

Abstract

We consider the first-kind Fredholm integral equatlon (A upsilon)(x) = f(x), x is an element of R+, where A is the Stieltjes transform defined as [GRAPHICS] Under some regularity assumptions on f we prove that the above problem is well-posed according to Tikhonov; that is, for any f in a given class of data there exists a unique solution upsilon of the above equation, and if \f(x)\ less than or equal to epsilon, For All x is an element of R+, for some positive is an element of then \v(y)\ less than or equal to alpha(epsilon), For All y is an element of [a, b], where alpha(epsilon) is a continuous non-decreasing function with alpha(0) = 0. An expression of the solution upsilon by means of a convergent Fourier series is also given.
15
281
290
First-kind Fredholm integral equations with kernel of Hankel type / A., Losi; Sacchetti, Andrea. - In: INVERSE PROBLEMS. - ISSN 0266-5611. - STAMPA. - 15(1999), pp. 281-290.
A., Losi; Sacchetti, Andrea
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11380/306371
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