In this paper we investigate generalized Gibbs measure (GGM) for $$p$$ -adic Hard-Core (HC) model with a countable set of spin values on Cayley tree order $$k\geq 2$$ . This is defined by parameters $$\lambda_i$$ , $$i\in \mathbb N$$ We analyze functional equation which provides the consistency condition finite-dimensional distributions. Each solutions defines GGM version Kolmogorov’s theorem. ...

We discuss the relevance of the classical and quantum rolling tachyons inflation in the frame of the standard, p-adic and adelic minisuperspace quantum cosmology. The field theory of tachyon matter proposed by Sen in a zero-dimensional version suggested by Kar leads to a model of a particle moving in a constant external field with quadratic damping. We calculate the exact quantum propagator of ...

We study spanning properties of a family functions translated along simple model sets. characterize tight frame and dual generators for such irregular translates we apply the results to Gabor systems. use connection between sets almost periodic rely strongly on Poisson summations formula introduce so-called bracket product, which then plays crucial role in our approach. As corollary main obtain...

We construct the two-variable p-adic q-L-function which interpolates the generalized q-Bernoulli polynomials associated with primitive Dirichlet character χ. Indeed, this function is the q-extension of two-variable p-adic L-function due to Fox, corresponding to the case q = 1. Finally, we give some p-adic integral representation for this two-variable p-adic q-L-function and derive to q-extensio...

This review is devoted to dynamical systems in fields of p-adic numbers: origin of p-adic dynamics in p-adic theoretical physics (string theory, quantum mechanics and field theory, spin glasses), continuous dynamical systems and discrete dynamical systems. The main attention is paid to discrete dynamical systems iterations of maps in the field of p-adic numbers (or their algebraic extensions): ...

Fusion frames enable signal decompositions into weighted linear subspace components. For positive integers p, we introduce p-fusion frames, a sharpening of the notion of fusion frames. Tight p-fusion frames are closely related to the classical notions of designs and cubature formulas in Grassmann spaces and are analyzed with methods from harmonic analysis in the Grassmannians. We define the p-f...

An interesting method called Oblique Extension Principle (OEP) has been proposed in the literature for constructing compactly supported MRA tight and dual wavelet frames with high vanishing moments and high frame approximation orders. Many compactly supported MRA wavelet frames have been recently constructed from scalar refinable functions via OEP. Despite the great flexibility and popularity o...

Let p be a fixed prime. Throughout this paper Zp, Qp, C and Cp will, respectively, denote the ring of p-adic rational integers, the field of p-adic rational numbers, the complex number field and the completion of algebraic closure of Qp, cf. [1], [3], [6], [10]. Let vp be the normalized exponential valuation of Cp with |p|p = p −vp(p) = p. Kubota and Leopoldt proved the existence of meromorphic...

We discuss the concepts of pseudo-dual frames and approximately dual frames, and illuminate their relationship to classical frames. Approximately dual frames are easier to construct than the classical dual frames, and might be tailored to yield almost perfect reconstruction. For approximately dual frames constructed via perturbation theory, we provide a bound on the deviation from perfect recon...