Towards a theory of some unbounded linear operators on $p$-adic Hilbert spaces and applications

Toka Diagana

Displaying similar documents to “Towards a theory of some unbounded linear operators on $p$ -adic Hilbert spaces and applications”

Integrable functions for the Bernoulli measures of rank $1$

Hamadoun Maïga (2010)

Annales mathématiques Blaise Pascal

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In this paper, following the $p$ -adic integration theory worked out by A. F. Monna and T. A. Springer [, ] and generalized by A. C. M. van Rooij and W. H. Schikhof [, ] for the spaces which are not $σ$ -compacts, we study the class of integrable $p$ -adic functions with respect to Bernoulli measures of rank $1$ . Among these measures, we characterize those which are invertible and we give their inverse in the form of series.

A note on some expansions of p-adic functions

Grzegorz Szkibiel (1992)

Acta Arithmetica

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Introduction. Recently J. Rutkowski (see [3]) has defined the p-adic analogue of the Walsh system, which we shall denote by ${(ϕ ₘ)}_{m \in ℕ ₀}$ . The system ${(ϕ ₘ)}_{m \in ℕ ₀}$ is defined in the space C(ℤₚ,ℂₚ) of ℂₚ-valued continuous functions on ℤₚ. J. Rutkowski has also considered some questions concerning expansions of functions from C(ℤₚ,ℂₚ) with respect to ${(ϕ ₘ)}_{m \in ℕ ₀}$ . This paper is a remark to Rutkowski’s paper. We define another system ${(h ₙ)}_{n \in ℕ ₀}$ in C(ℤₚ,ℂₚ), investigate its properties and compare it to the system defined by Rutkowski....

P-adic Spaces of Continuous Functions II

Athanasios Katsaras (2008)

Annales mathématiques Blaise Pascal

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Necessary and sufficient conditions are given so that the space $C (X, E)$ of all continuous functions from a zero-dimensional topological space $X$ to a non-Archimedean locally convex space $E$ , equipped with the topology of uniform convergence on the compact subsets of $X$ , to be polarly absolutely quasi-barrelled, polarly $ℵ_{o}$ -barrelled, polarly $ℓ^{\infty}$ -barrelled or polarly $c_{o}$ -barrelled. Also, tensor products of spaces of continuous functions as well as tensor products of certain $E^{'}$ -valued measures are investigated. ...

Links between cyclotomic and ${GL}_{2}$ Iwasawa theory.

Coates, John, Schneider, Peter, Sujatha, Ramdorai (2003)

Documenta Mathematica

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A correspondence for the generalized Hecke algebra of the metaplectic cover $\bar{S L (2, F)}$ , $F$ $p$ -adic.

Joyner, David (1998)

The New York Journal of Mathematics [electronic only]

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Completely faithful Selmer groups over Kummer extensions.

Hachimori, Yoshitaka, Venjakob, Otmar (2003)

Documenta Mathematica

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The Lucas congruence for Stirling numbers of the second kind

Roberto Sánchez-Peregrino (2000)

Acta Arithmetica

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0. Introduction. The numbers introduced by Stirling in 1730 in his Methodus differentialis [11], subsequently called “Stirling numbers” of the first and second kind, are of the greatest utility in the calculus of finite differences, in number theory, in the summation of series, in the theory of algorithms, in the calculation of the Bernstein polynomials [9]. In this study, we demonstrate some properties of Stirling numbers of the second kind similar to those satisfied by binomial coefficients;...

On character and chain conditions in images of products

Murray Bell (1998)

Fundamenta Mathematicae

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A scadic space is a Hausdorff continuous image of a product of compact scattered spaces. We complete a theorem begun by G. Chertanov that will establish that for each scadic space X, χ(X) = w(X). A ξ-adic space is a Hausdorff continuous image of a product of compact ordinal spaces. We introduce an either-or chain condition called Property $R_{λ}^{'}$ which we show is satisfied by all ξ-adic spaces. Whereas Property $R_{λ}^{'}$ is productive, we show that a weaker (but more natural) Property $R_{λ}$ is not productive....

Growth of the product $\prod_{j = 1}^{n} (1 - x^{a_{j}})$

J. P. Bell, P. B. Borwein, L. B. Richmond (1998)

Acta Arithmetica

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We estimate the maximum of $\prod_{j = 1}^{n} | 1 - x^{a_{j}} |$ on the unit circle where 1 ≤ a₁ ≤ a₂ ≤ ... is a sequence of integers. We show that when $a_{j}$ is $j^{k}$ or when $a_{j}$ is a quadratic in j that takes on positive integer values, the maximum grows as exp(cn), where c is a positive constant. This complements results of Sudler and Wright that show exponential growth when $a_{j}$ is j. In contrast we show, under fairly general conditions, that the maximum is less than $2^{n} / n^{r}$ , where r is an arbitrary positive number. One consequence...

Displaying similar documents to “Towards a theory of some unbounded linear operators on p -adic Hilbert spaces and applications”

Displaying similar documents to “Towards a theory of some unbounded linear operators on $p$ -adic Hilbert spaces and applications”