On an integral operator in the space of functions with bounded variation. II.
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Štefan Schwabik (1977)
Časopis pro pěstování matematiky
Stephen Joe, Ian H. Sloan (1986)
Numerische Mathematik
Bernd Hofmann (1984)
Banach Center Publications
A. T. Bharucha-Reid, L. Arnold (1969)
Applicationes Mathematicae
Štefan Schwabik (1971)
Commentationes Mathematicae Universitatis Carolinae
Shulaia, D. (1997)
Georgian Mathematical Journal
Nguyen Van Mau, Nguyen Minh Tuan (1996)
Annales Polonici Mathematici
We deal with a class of integral equations on the unit circle in the complex plane with a regular part and with rotations of the form (*) x(t) + a(t)(Tx)(t) = b(t), where and are of the form (3) below. We prove that under some assumptions on analytic continuation of the given functions, (*) is a singular integral equation for m odd and is a Fredholm equation for m even. Further, we prove that T is an algebraic operator with characteristic polynomial . By means of the Riemann boundary value...
Chabrowski, J.H. (1988)
International Journal of Mathematics and Mathematical Sciences
Wolfgang Borchers, Werner Varnhorn (1993)
Mathematische Zeitschrift
Wolfgang Hackbusch, Stefan A. Sauter (1993)
Applications of Mathematics
In the present paper we describe, how to use the Galerkin-method efficiently in solving boundary integral equations. In the first part we show how the elements of the system matrix can be computed in a reasonable time by using suitable coordinate transformations. These techniques can be applied to a wide class of integral equations (including hypersingular kernels) on piecewise smooth surfaces in 3-D, approximated by spline functions of arbitrary degree. In the second part we show, how to use the...
M. Kwapisz, J. Turo (1979)
Aequationes mathematicae
Bogdan Rzepecki (1975)
Annales Polonici Mathematici
Ramón Gutiérrez Jáimez, Mariano J. Valderrama Bonnet (1987)
Trabajos de Estadística
We discuss the influence of the transformation {X(t)} → {f(t) X(τ(t))} on the Karhunen-Loève expansion of {X(t)}. Our main result is that, in general, the Karhunen-Loève expansion of {X(t)} with respect to Lebesgue's measure is transformed in the Karhunen-Loève expansion of {f(t) X(τ(t))} with respect to the measure f-2(t)dτ(t). Applications of this result are given in the case of Wiener process, Brownian bridge, and Ornstein-Uhlenbeck process.
Kress, Rainer (1999)
Zeitschrift für Analysis und ihre Anwendungen
R. Plato, G. Vainikko (1990)
Numerische Mathematik
I. Gohberg, E. Azoff, K. Clancey (1979/1980)
Manuscripta mathematica
R. Vermiglio (1992)
Numerische Mathematik
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