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6 papers · 1 filter
On approximation of p-adic numbers by p-adic algebraic numbers
Victor Beresnevich, Vasili Bernik, Ella Kovalevskaya
A complete p-adic Khintchine type theorem for approximation by p-adic algebraic numbers is established.
Umbral Calculus in Positive Characteristic
Anatoly N. Kochubei
An umbral calculus over local fields of positive characteristic is developed on the basis of a relation of binomial type satisfied by the Carlitz polynomials. Orthonormal bases in…
Strongly Nonlinear Differential Equations with Carlitz Derivatives over a Function Field
Anatoly N. Kochubei
In earlier papers the author studied some classes of equations with Carlitz derivatives for -linear functions, which are the natural function field counterparts of lin…
On the Cauchy Problem for Differential Equations in a Banach Space over the Field of p-Adic Numbers. II
Myroslav L. Gorbachuk, Valentyna I. Gorbachuk
For an operator-differential equation of the form , where is a closed linear operator on a Banach space over the the field of -adic numbers, the necessar…
On the Cauchy Problem for Differential Equations in a Banach Space over the Field of p-Adic Numbers. I
Myroslav L. Gorbachuk, Valentyna I. Gorbachuk
For the Cauchy problem for an operator differential equation of the form , where is a closed linear operator on a Banach space over the completion of an algebrai…
Differential Equations for -Linear Functions, II: Regular Singularity
Anatoly N. Kochubei
We study some classes of equations with Carlitz derivatives for -linear functions, which are the natural function field counterparts of linear ordinary differential equations…