Padé approximants in complex points revisited.
Padé approximations to certain power series.
Pervasive algebras on planar compacts
We characterize compact sets in the Riemann sphere not separating for which the algebra of all functions continuous on and holomorphic on , restricted to the set , is pervasive on .
Pointwise and locally uniform convergence of holomorphic and harmonic functions.
Pointwise and locally uniform convergence of holomorphic and harmonic functions
We shall characterize the sets of locally uniform convergence of pointwise convergent sequences. Results obtained for sequences of holomorphic functions by Hartogs and Rosenthal in 1928 will be generalized for many other sheaves of functions. In particular, our Hartogs-Rosenthal type theorem holds for the sheaf of solutions to the second order elliptic PDE's as well as it has applications to the theory of harmonic spaces.
Polyanalytic Besov spaces and approximation by dilatations
Using partial derivatives and , we introduce Besov spaces of polyanalytic functions in the open unit disk, as well as in the upper half-plane. We then prove that the dilatations of functions in certain weighted polyanalytic Besov spaces converge to the same functions in norm. When restricted to the open unit disk, we prove that each polyanalytic function of degree can be approximated in norm by polyanalytic polynomials of degree at most .
Polynomial approximations and universality
We give another version of the recently developed abstract theory of universal series to exhibit a necessary and sufficient condition of polynomial approximation type for the existence of universal elements. This certainly covers the case of simultaneous approximation with a sequence of continuous linear mappings. In the case of a sequence of unbounded operators the same condition ensures existence and density of universal elements. Several known results, stronger statements or new results can be...
Possibility of Complex Asymptotic Approximation on Closed Sets.
Power series and zeroes of trinomial equations.
Power series and zeroes of trinomial equations. (Summary).
Power Series Equivalent to Rational Functions: A Shifting-Origin Kronecker Type Theorem, and Normality of Padé Tables.
Pseudo shift operators with large images
We give suitable conditions for the existence of many holomorphic functions f on a disc such that the image of any nonempty open subset under the action of pseudo shift operators on f is arbitrarily large. This generalizes an earlier result about images of derivatives and completes another one on infinite order differential operators.