Displaying similar documents to “Solution of Cauchy-type singular integral equations of the first kind with zeros of Jacobi polynomials as interpolation nodes.”

Interpolation formulas for functions of exponential type

Josef Kofroň, Emílie Moravcová (2001)

Applications of Mathematics

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In the paper we present a derivative-free estimate of the remainder of an arbitrary interpolation rule on the class of entire functions which, moreover, belong to the space L ( - ∞ , + ∞ ) 2 . The theory is based on the use of the Paley-Wiener theorem. The essential advantage of this method is the fact that the estimate of the remainder is formed by a product of two terms. The first term depends on the rule only while the second depends on the interpolated function only. The obtained estimate of the...

Interpolation operators on the space of holomorphic functions on the unit circle

Josef Kofroň (2001)

Applications of Mathematics

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The aim of the paper is to get an estimation of the error of the general interpolation rule for functions which are real valued on the interval [ - a , a ] , a ∈ ( 0 , 1 ) , have a holomorphic extension on the unit circle and are quadratic integrable on the boundary of it. The obtained estimate does not depend on the derivatives of the function to be interpolated. The optimal interpolation formula with mutually different nodes is constructed and an error estimate as well as the rate of convergence are obtained....