منابع مشابه
2 A CERTAIN p - ADIC SPECTRAL THEOREM
3 ABSTRACT. We extend a p-adic spectral theorem of M. M. Vishik to a certain class of p-adic Banach algebras. This class includes inductive limits of finite-dimensional p-Banach algebras of the form B(X), where X is a p-adic Banach space of the form X ≃ Ω p (J), J being a finite nonempty set. In particular, we present a p-adic spectral theorem for p-adic UHF algebras and p-adic TUHF algebras (T...
متن کاملSome p-adic differential equations
We investigate various properties of p-adic differential equations which have as a solution an analytic function of the form Fk(x) = ∑ n≥0 n!Pk(n)x , where Pk(n) = n +Ck−1n k−1+· · ·+C0 is a polynomial in n with Ci ∈ Z (in a more general case Ci ∈ Q or Ci ∈ Cp) , and the region of convergence is | x |p< p 1 p−1 . For some special classes of Pk(n), as well as for the general case, the existence ...
متن کاملIrrationality of Certain p - adic Periods for Small p
Apéry’s proof [13] of the irrationality of ζ(3) is now over 25 years old, and it is perhaps surprising that his methods have not yielded any significant new results (although further progress has been made on the irrationality of zeta values [1, 14]). Shortly after the initial proof, Beukers produced two elegant reinterpretations of Apéry’s arguments; the first using iterated integrals and Lege...
متن کاملSimultaneous diagonal equations over p-adic fields
with coefficients aij in O. Write the degree as k = pm with p m. A solution x = (x1, . . . , xN) ∈ K is called non-trivial if at least one xj is non-zero. It is a special case of a conjecture of Emil Artin that (∗) has a non-trivial solution whenever N > Rk. This conjecture has been verified by Davenport and Lewis for a single diagonal equation over Qp and for a pair of equations of odd degree ...
متن کاملp-adic Shearlets
The field $Q_{p}$ of $p$-adic numbers is defined as the completion of the field of the rational numbers $Q$ with respect to the $p$-adic norm $|.|_{p}$. In this paper, we study the continuous and discrete $p-$adic shearlet systems on $L^{2}(Q_{p}^{2})$. We also suggest discrete $p-$adic shearlet frames. Several examples are provided.
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1984
ISSN: 0022-314X
DOI: 10.1016/0022-314x(84)90092-1