On a bounded increasing power series

κ-bounded Exponential-Logarithmic Power Series Fields

In [K–K–S] it was shown that fields of generalized power series cannot admit an exponential function. In this paper, we construct fields of generalized power series with bounded support which admit an exponential. We give a natural definition of an exponential, which makes these fields into models of real exponentiation. The method allows to construct for every κ regular uncountable cardinal, 2...

Ela a Note on Power Bounded Matrices

We say A is convergent to the matrix X = [xij ] if the sequences (A )ij converge to xij as k → ∞. A matrix is convergent if it is convergent to some matrix. This is a special case of convergence as defined in [4, Definition 10.1], for the matrix sequence {A,A, A, . . . }. In particular, we say A is zero convergent when A is convergent to the zero matrix. We distinguish between convergence and z...

A note on power bounded matrices

On Interpolating Power Series

We derive a simple error estimate for equally spaced, polynomial interpolation of power series that does not require the uniform bounds on derivatives of the Cauchy remainder. The key steps are expressing Newton coefficients in terms of Stirling numbers S(i, j) of the second kind and applying the concavity of lnS(i, j).

On D0L power series

We study D0L power series. We show how elementary morphisms introduced by Ehrenfeucht and Rozenberg can be used in connection with power series, characterize the sequences of rational numbers and integers which can be appear as coe cients in D0L power series and establish various decidability results. TUCS Research Group Mathematical Structures of Computer Science