On the degree of polynomial approximation to harmonic and analytic functions

On the Degree of Polynomial Approximation to Harmonic and Analytic Functions

extensions of some polynomial inequalities to the polar derivative

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Best Approximation in the Mean by Analytic and Harmonic Functions

For n ≥ 2, let Bn denote the unit ball in R, and for p ≥ 1 let L denote the Banach space of p-summable functions on Bn. Let L p h(Bn) denote the subspace of harmonic functions on Bn that are p-summable. When n = 2, we often write D instead of B2, and we let A denote the Bergman space of analytic functions in L. Let ω be a function in L. We are interested in finding the best approximation to ω i...

Note on Degree of Approximation to Analytic Functions by Rational Functions with Preassigned Poles.

The purpose of this note is to establish several results, especially Theorem 1 below, relative to degree of approximation to analytic functions and their boundary values, the latter assumed to satisfy certain continuity conditions (Lipschitz conditions, etc.). The present results are closely related to, but more general than, results due to Sewell' and Elliott;2 the results have application to ...

Note on Polynomial Interpolation to Analytic Functions.

last upper and lower molars. Chumashius balchi cannot, therefore, be regarded as occurring in the direct line of development leading upward to the Recent tarsier. In lower dental formula Chumashius exhibits a closer relationship to Omomys and Hemi4codon than to Anaptomorphus and Tetonius. The character of the lower posterior premolars in Uintanius suffice to remove this Bridger genus from any c...