-adic analytic interpolation
Padé approximants in complex points revisited.
Padé approximations to certain power series.
Parameter Tuning and Repeated Application of the IMT-type Transformation in Numerical Quadrature.
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 .
Pick functions related to entire functions having negative zeros.
Pick-Nevanlinna interpolation on finitely-connected domains
Let Ω be a domain in the complex plane bounded by m+1 disjoint, analytic simple closed curves and let be n+1 distinct points in Ω. We show that for each (n+1)-tuple of complex numbers, there is a unique analytic function B such that: (a) B is continuous on the closure of Ω and has constant modulus on each component of the boundary of Ω; (b) B has n or fewer zeros in Ω; and (c) , 0 ≤ j ≤ n.
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.
Premiers pas en calcul étranger
Cet exposé est une introduction au calcul étranger d’Écalle, c’est-à-dire au calcul des obstructions à la sommabilité de Borel d’une grande classe de séries formelles, les fonctions résurgentes d’Écalle. La théorie d’Écalle éclaire d’un jour neuf le célèbre phénomène de Stokes qui est illustré ici dans le contexte de la méthode du col.
Problème des moments matriciels sur la droite : construction d'une famille de solutions et questions d'unicité
Product Integration of Piecewise Continuous Integrands Based on Cubic Spline Interpolation at Equally Spaced Nodes.
Product Integration of Singular Integrands Based on Cubic Spline Interpolation at Equally Spaced Nodes.
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.