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

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

Toka Diagana (2005)

Annales mathématiques Blaise Pascal

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We are concerned with some unbounded linear operators on the so-called p -adic Hilbert space 𝔼 ω . Both the Closedness and the self-adjointness of those unbounded linear operators are investigated. As applications, we shall consider the diagonal operator on 𝔼 ω , and the solvability of the equation A u = v where A is a linear operator on 𝔼 ω .

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.

The Heisenberg uncertainty relation in harmonic analysis on p -adic numbers field

Cui Minggen, Zhang Yanying (2005)

Annales mathématiques Blaise Pascal

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In this paper, two important geometric concepts–grapical center and width, are introduced in p -adic numbers field. Based on the concept of width, we give the Heisenberg uncertainty relation on harmonic analysis in p -adic numbers field, that is the relationship between the width of a complex-valued function and the width of its Fourier transform on p -adic numbers field.

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 ∈ ℕ ₀ . The system ( ϕ ₘ ) m ∈ 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 ∈ ℕ ₀ . This paper is a remark to Rutkowski’s paper. We define another system ( h ₙ ) n ∈ ℕ ₀ in C(ℤₚ,ℂₚ), investigate its properties and compare it to the system defined by Rutkowski....

Signed Selmer groups over p -adic Lie extensions

Antonio Lei, Sarah Livia Zerbes (2012)

Journal de Théorie des Nombres de Bordeaux

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Let E be an elliptic curve over ℚ with good supersingular reduction at a prime p ≥ 3 and a p = 0 . We generalise the definition of Kobayashi’s plus/minus Selmer groups over ℚ ( μ p ∞ ) to p -adic Lie extensions K ∞ of ℚ containing ℚ ( μ p ∞ ) , using the theory of ( ϕ , Γ ) -modules and Berger’s comparison isomorphisms. We show that these Selmer groups can be equally described using Kobayashi’s conditions via the theory of overconvergent power series. Moreover, we show that such an approach gives the usual Selmer groups in the...

On the linear independence of p -adic L -functions modulo p

Bruno Anglès, Gabriele Ranieri (2010)

Annales de l’institut Fourier

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Let p ≥ 3 be a prime. Let n ∈ ℕ such that n ≥ 1 , let χ 1 , ... , χ n be characters of conductor d not divided by p and let ω be the Teichmüller character. For all i between 1 and n , for all j between 0 and ( p - 3 ) / 2 , set θ i , j = χ i ω 2 j + 1 if χ i is odd ; χ i ω 2 j if χ i is even . Let K = ℚ p ( χ 1 , ... , χ n ) and let π be a prime of the valuation ring 𝒪 K of K . For all i , j let f ( T , θ i , j ) be the Iwasawa series associated to θ i , j and f ( T , θ i , j ) ¯ its reduction modulo ( π ) . Finally let 𝔽 p ¯ be an algebraic closure of 𝔽 p . Our main result is that if the characters χ i are all distinct modulo ( π ) , then 1 and the series...