Consider the fractional ARIMA time series with innovations that have innnite variance. This is a nite parameter model which exhibits both long-range dependence (long memory) and high variability. We prove the consistency of an estimator of the unknown parameters which is based on the periodogram and derive its asymptotic distribution. This shows that the results of Mikosch, Gadrich, Kl uppelber...

To a compact hyperbolic Riemann surface, we associate a finitely summable spectral triple whose underlying topological space is the limit set of a corresponding Schottky group, and whose “Riemannian” aspect (Hilbert space and Dirac operator) encode the boundary action through its Patterson-Sullivan measure. We prove that the ergodic rigidity theorem for this boundary action implies that the zet...

It is proved, under Martin’s Axiom, that all (ω1, ω1) gaps in P(N) / fin are indestructible in any forcing extension by a separable measure algebra. This naturally leads to a new type of gap, a summable gap. The results of these investigations have applications in Descriptive Set Theory. For example, it is shown that under Martin’s Axiom the Baire categoricity of all ∆3 non-∆ 1 3-complete sets ...

In this paper, the idea of lacunary [Formula: see text]-statistical convergent sequence spaces is discussed which is defined by a Musielak-Orlicz function. We study relations between lacunary [Formula: see text]-statistical convergence with lacunary [Formula: see text]-summable sequences. Moreover, we study the [Formula: see text]-lacunary statistical convergence in probabilistic normed space a...

The incomplete Gamma function γ(α, x) and its associated functions γ(α, x+) and γ(α, x−) are defined as locally summable functions on the real line and some convolutions and neutrix convolutions of these functions and the functions x and x − are then found.

In the first part we have shown that, for L2-approximation of functions from a separable Hilbert space in worst-case setting, linear algorithms based on function values are almost as powerful arbitrary if widths square-summable. That is, they achieve same polynomial rate convergence. this sequel, prove similar result Banach spaces and other classes functions.

In this study, we are concerned with introducing Weyl-Titchmarsh theory for a class of dynamic linear Hamiltonian nabla systems over a half-line on Sturmian time scales. After developing fundamental properties of solutions and regular spectral problems, we introduce the corresponding maximal and minimal operators for the system. Matrix disks are constructed and proved to be nested and converge ...

In this paper discrete time-varying systems are considered. The study of spectral properties in a time-varying framework is performed by defining a suitable operator on the Hilbert space of square summable sequences. This setting gives a parameterization of square summable symmetric solutions for time-varying Riccati equations.

In 1911, Steinhaus presented the following theorem: if A is a regular matrix then there exists a sequence of 0’s and 1’s which is not A-summable. In 1943, R. C. Buck characterized convergent sequences as follows: a sequence x is convergent if and only if there exists a regular matrix A which sums every subsequence of x. In this paper, definitions for “subsequences of a double sequence” and “Pri...

we obtain sufficient conditions for the series σanλn to be absolutely summable of order k by atriangular matrix.