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Ergodic dynamical systems over the cartesian power of the ring of p-adic integers
Pleiades Publishing Ltd - Tập 6 - Trang 333-336 - 2014
For any 1-lipschitz ergodic map F: ℤ ↦ ℤ , k >1 ∈ ℕ, there are 1-lipschitz
ergodic map G: ℤ p ↦ ℤ p and two bijections H k , T k, P that $G = H_k \circ
T_{k,P} \circ F \circ H_k^{ - 1} andF = H_k^{ - 1} \circ T_{k,P - 1} \circ G
\circ H_k $ ....
Sparse p-adic data coding for computationally efficient and effective big data analytics
Pleiades Publishing Ltd - Tập 8 Số 3 - Trang 236-247 - 2016
We develop the theory and practical implementation of p-adic sparse coding of
data. Rather than the standard, sparsifying criterion that uses the L 0
pseudo-norm, we use the p-adic norm.We require that the hierarchy or tree be
node-ranked, as is standard practice in agglomerative and other hierarchical
clustering, but not necessarily with decision trees. In order to structure the
data, all computa...
On countable unions of nonmeager sets in hereditarily Lindelöf spaces
Pleiades Publishing Ltd - Tập 3 - Trang 1-6 - 2011
It is well known that any Vitali set on the real line ℝ does not possess the
Baire property. The same is valid for finite unions of Vitali sets. What can be
said about infinite unions of Vitali sets? Let S be a Vitali set, S r be the
image of S under the translation of ℝ by a rational number r and F = {S r : r is
rational}. We prove that for each non-empty proper subfamily F′ of F the union
∪F′ do...
Representation Theorems for Operators on Free Banach Spaces of Countable Type
Pleiades Publishing Ltd - Tập 11 - Trang 21-36 - 2019
This work will be centered in commutative Banach subalgebras of the algebra of
bounded linear operators defined on free Banach spaces of countable type. The
main goal of this work will be to formulate a representation theorem for these
operators through integrals defined by spectral measures type. In order to get
this objective, we will show that, under special conditions, each one of these
algebr...
Zeros of p-adic differential polynomials
Pleiades Publishing Ltd - Tập 6 - Trang 166-170 - 2014
Let $$\mathbb{K}$$ be a complete algebraically closed p-adic field of
characteristic zero. We consider a differential polynomial of the form F = a n f
n f (k) + a n−1 f n−1 + ... + a 0 where the a j are small functions with respect
to f and f is a meromorphic function in $$\mathbb{K}$$ or inside an open disk.
Using p-adic methods, we can prove that when N(r, f) = S(r, f), then F must have
infinite...
Cognitive processes of the brain: An ultrametric model of information dynamics in unconsciousness
Pleiades Publishing Ltd - Tập 6 - Trang 293-302 - 2014
We discuss differences in mathematical representations of the physical and
mental worlds. Following Aristotle, we present the mental space as discrete,
hierarchic, and totally disconnected topological space. One of the basic models
of such spaces is given by ultrametric spaces and more specially by m-adic
trees. We use dynamical systems in such spaces to model flows of unconscious
information at d...
On Quasisymmetric Mappings Between Ultrametric Spaces
Pleiades Publishing Ltd - Tập 13 - Trang 231-238 - 2021
In 1980 P. Tukia and J. Väisälä in seminal paper [23] extended a concept of
quasisymmetric mapping known from the theory of quasiconformal mappings to the
case of general metric spaces. They also found an estimation for the ratio of
diameters of two subsets which are images of two bounded subsets of a metric
space under a quasisymmetric mapping. We improve this estimation for the case of
ultrametr...
Factorizations of relative extremal projectors
Pleiades Publishing Ltd - Tập 7 - Trang 276-290 - 2015
We survey earlier results on factorizations of extremal projectors and relative
extremal projectors and present preliminary results on non-commutative
factorizations of relative extremal projectors: we deduce the existence of such
factorizations for sl4 and sl5.
A theorem on weighted means in non-archimedean fields
Pleiades Publishing Ltd - Tập 2 - Trang 363-367 - 2010
K denotes a complete, non-trivially valued, non-archimedean field. Infinite
matrices, sequences and series have entries in K. In this paper, we prove an
interesting result, which gives an equivalent formulation of summability by
weighted mean methods. Incidentally this result includes the non-archimedean
analogue of a theorem proved by Móricz and Rhoades (see [2], Theorem MR, p.188).
Hörmander Classes of Pseudo-Differential Operators over the Compact Group of p-Adic Integers
Pleiades Publishing Ltd - Tập 12 - Trang 134-162 - 2020
The purpose of this paper is to introduce new definitions of Hörmander classes
for pseudo-differential operators over the compact group of p-adic integers. Our
definitions possesses a symbolic calculus, asymptotic expansions and
parametrices, together with an interesting relation with the infinite matrices
algebras studied by K. Gröchenig and S. Jaffard. Also, we show how our
definition of Hörmand...
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