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Advances in ultrametric analysis : 14th International Conference, p-adic Functional Analysis, June 30-July 4, 2016, Université d'Auvergne, Aurillac, France
This book contains the proceedings of the 14th International Conference on $p$-adic Functional Analysis, held from June 30-July 5, 2016, at the Universite d'Auvergne, Aurillac, France. Articles included in this book feature recent developments in various areas of non-Archimedean analysis: summation of p -adic series, rational maps on the projective line over Q p , non-Archimedean Hahn-Banach theorems, ultrametric Calkin algebras, G -modules with a convex base, non-compact Trace class operators and Schatten-class operators in p -adic Hilbert spaces, algebras of strictly differentiable functions, inverse function theorem and mean value theorem in Levi-Civita fields, ultrametric spectra of commutative non-unital Banach rings, classes of non-Archimedean Köthe spaces, p -adic Nevanlinna theory and applications, and sub-coordinate representation of p -adic functions. Moreover, a paper on the history of p -adic analysis with a comparative summary of non-Archimedean fields is presented.Through a combination of new research articles and a survey paper, this book provides the reader with an overview of current developments and techniques in non-Archimedean analysis as well as a broad knowledge of some of the sub-areas of this exciting and fast-developing research area.
eBook
Advances in Ultrametric Analysis
This book contains the proceedings of the 14th International Conference on p-adic Functional Analysis, held from June 30-July 4, 2016, at the Universit d'Auvergne, Aurillac, France. Articles included in this book feature recent developments in various areas of non-Archimedean analysis: summation of p-adic series, rational maps on the projective line over \\mathbb{Q}p, non-Archimedean Hahn-Banach theorems, ultrametric Calkin algebras, G-modules with a convex base, non-compact Trace class operators and Schatten-class operators in p-adic Hilbert spaces, algebras of strictly differentiable functions, inverse function theorem and mean value theorem in Levi-Civita fields, ultrametric spectra of commutative non-unital Banach rings, classes of non-Archimedean K the spaces, p-adic Nevanlinna theory and applications, and sub-coordinate representation of p-adic functions. Moreover, a paper on the history of p-adic analysis with a comparative summary of non-Archimedean fields is presented. Through a combination of new research articles and a survey paper, this book provides the reader with an overview of current developments and techniques in non-Archimedean analysis as well as a broad knowledge of some of the sub-areas of this exciting and fast-developing research area.
eBook
Spectral expansions of non-self-adjoint generalized Laguerre semigroups
We provide the spectral expansion in a weighted Hilbert space of a substantial class of invariant non-self-adjoint and non-local
Markov operators which appear in limit theorems for positive-valued Markov processes. We show that this class is in bijection with a
subset of negative definite functions and we name it the class of generalized Laguerre semigroups. Our approach, which goes beyond the
framework of perturbation theory, is based on an in-depth and original analysis of an intertwining relation that we establish between
this class and a self-adjoint Markov semigroup, whose spectral expansion is expressed in terms of the classical Laguerre polynomials. As
a by-product, we derive smoothness properties for the solution to the associated Cauchy problem as well as for the heat kernel. Our
methodology also reveals a variety of possible decays, including the hypocoercivity type phenomena, for the speed of convergence to
equilibrium for this class and enables us to provide an interpretation of these in terms of the rate of growth of the weighted Hilbert
space norms of the spectral projections. Depending on the analytic properties of the aforementioned negative definite functions, we are
led to implement several strategies, which require new developments in a variety of contexts, to derive precise upper bounds for these
norms.
eBook
On the Growth Orders and Types of Biregular Functions
One of the main aims of Clifford analysis is to study the growth properties of regular functions. Biregular functions are a well-known generalization of regular functions. In this paper, the growth orders and types of biregular functions are studied. First, generalized growth orders and types of biregular functions are defined in the context of Clifford analysis. Then, using the methods of Wiman and Valiron, generalized Lindelöf–Pringsheim theorems are proved, which show the relationship between growth orders, growth types, and Taylor series. These connections allow us to calculate the growth order and determine the type of biregular functions.
Journal Article
Majorization Problems for Subclasses of Meromorphic Functions Defined by the Generalized q-Sălăgean Operator
Using the generalized q-Sălăgean operator, we introduce a new class of meromorphic functions in a punctured unit disk U∗ and investigate a majorization problem associated with this class. The principal tool employed in this analysis is the recently established q-Schwarz–Pick lemma. We investigate a majorization problem for meromorphic functions when the functions of the right hand side of the majorization belongs to this class. The main tool for this investigation is the generalization of Nehari’s lemma for the Jackson’s q-difference operator ∂q given recently by Adegani et al.
Journal Article
Asymptotic Theory for Multivariate Nonparametric Quantile Regression with Stationary Ergodic Functional Covariates and Missing-at-Random Responses
Quantiles are among the most fundamental constructs in probability theory and statistics, intrinsically linked to order structures, stochastic dominance, and the principles of robust statistical inference. Although the univariate theory of quantiles is by now classical and well developed, their generalization to multivariate settings remains mathematically subtle and methodologically demanding. In particular, extending the notion of “location within a distribution” beyond one dimension raises delicate questions of geometry, ordering, and equivariance. Within this landscape, the spatial—or geometric—formulation of multivariate quantiles has emerged as a rigorous and conceptually unifying framework capable of reconciling these issues. In this work we advance this paradigm by introducing a kernel-based estimation procedure for nonparametric conditional geometric quantiles of a multivariate response Y∈Rq (q≥2) given a functional covariate X that takes values in an infinite-dimensional space. The data are assumed to form a strictly stationary and ergodic process, while the responses may be subject to a missing-at-random mechanism, a feature of substantial practical relevance. Our analysis establishes strong consistency of the proposed estimator, characterizes its optimal convergence rate, and derives its asymptotic distribution. These limit theorems, in turn, provide the theoretical foundation for constructing asymptotically valid confidence regions and for performing inference in multivariate quantile regression with functional covariates. The theoretical developments rest on natural complexity conditions for the involved functional classes together with mild smoothness and regularity assumptions. This balance between generality and mathematical precision ensures that the resulting methodology is not only robust in a rigorous probabilistic sense but also widely applicable to contemporary problems in high-dimensional and functional data analysis. The proposed methodology is numerically investigated through simulations and is implemented in a real data application.
Journal Article
A Note on Some Generalized Hypergeometric Reduction Formulas
Herein, we calculate reduction formulas for some generalized hypergeometric functions m+1Fmz in terms of elementary functions as well as incomplete beta functions. For this purpose, we calculate the n-th order derivative of the function zγBzα,β with respect to z. As corollaries, we obtain reduction formulas of these m+1Fmz functions for argument unity in terms of elementary functions, as well as beta functions.
Journal Article
Characterization Results on Lifetime Distributions by Scaled Reliability Measures Using Completeness Property in Functional Analysis
In this article, using the scaled (weighted) residual life variable, some scaled measures, the scaled mean residual life and the scaled hazard rate, are introduced. Several scales are considered as examples of the derivation of the scaled measures. The measures are developed for the case of a weighted residual life at a random time, and it is shown that the measures are scale-free in these cases. This property proves useful in situations where a relative comparison of the lifetime distribution is studied. Some characterization properties are derived in terms of scaled measures evaluated at some sequences of random time points that follow a typical distribution. Examples are used to illustrate, examine, and satisfy the obtained characterizations.
Journal Article