A Note on Rational $$L^p$$ L p Approximation on Jordan Curves

A Note on Approximation by Rational Functions

The theory of the approximation by rational functions on point sets E of the js-plane (z = x+iy) has been summarized by J. L. Walsh who himself has proved a great number of important theorems some of which are fundamental. The results concern both the case when E is bounded and when E extends to infinity. In the present note a Z^-theory (0<p< oo) will be given for the following point sets exten...

Discrete Rational Lp Approximation

In this paper, the problem of approximating a function defined on a finite subset of the real line by a family of generalized rational functions whose numerator and denominator spaces satisfy the Haar conditions on some closed interval [a, b] containing the finite set is considered. The pointwise closure of the family restricted to the finite set is explicitly determined. The representation obt...

A Note on Weighted Composition Operators on L^p-Spaces

A note on simultaneous Diophantine approximation on planar curves

Let Sn(ψ1, . . . , ψn) denote the set of simultaneously (ψ1, . . . , ψn)–approximable points in Rn and S∗ n (ψ) denote the set of multiplicatively ψ–approximable points in Rn. Let M be a manifold in Rn. The aim is to develop a metric theory for the sets M∩Sn(ψ1, . . . , ψn) and M∩S∗ n (ψ) analogous to the classical theory in whichM is simply Rn. In this note, we mainly restrict our attention to...

A note on superspecial and maximal curves

In this note we review a simple criterion, due to Ekedahl, for superspecial curves defined over finite fields.Using this we generalize and give some simple proofs for some well-known superspecial curves.