Family Of Linear Operators Research Articles

Inclusion properties for analytic functions of $ q $-analogue multiplier-Ruscheweyh operator

<abstract><p>The results of this work have a connection with the geometric function theory and they were obtained using methods based on subordination along with information on $ \mathfrak{q} $-calculus operators. We defined the $ \mathfrak{q} $-analogue of multiplier- Ruscheweyh operator of a certain family of linear operators $ I_{\mathfrak{q}, \mu }^{s}(\lambda, \ell) \mathfrak{f}(\varsigma) \; (s\in \mathbb{N}_{0} = \mathbb{N}\cup \{0\}, \mathbb{ N} = \left\{ 1, 2, 3, ..\right\}; \ell, \lambda, \mu \geq 0, 0 < \mathfrak{q} < 1) $. Our major goal was to build some analytic function subclasses using $ I_{ \mathfrak{q}, \mu }^{s}(\lambda, \ell)\mathfrak{f}(\varsigma) $ and to look into various inclusion relationships that have integral preservation features.</p></abstract>

On Generalizations of the Close-to-Convex Functions Associated with q-Srivastava–Attiya Operator

The study of the q-analogue of the classical results of geometric function theory is currently of great interest to scholars. In this article, we define generalized classes of close-to-convex functions and quasi-convex functions with the help of the q-difference operator. Moreover, by using the q-analogues of a certain family of linear operators, the classes Kq,bsh, K˜q,sbh, Qq,bsh, and Q˜q,sbh are introduced. Several interesting inclusion relationships between these newly defined classes are discussed, and the invariance of these classes under the q-Bernadi integral operator was examined. Furthermore, some special cases and useful consequences of these investigations were taken into consideration.

Localized Shape Modelling with Global Coherence: An Inverse Spectral Approach

AbstractMany natural shapes have most of their characterizing features concentrated over a few regions in space. For example, humans and animals have distinctive head shapes, while inorganic objects like chairs and airplanes are made of well‐localized functional parts with specific geometric features. Often, these features are strongly correlated – a modification of facial traits in a quadruped should induce changes to the body structure. However, in shape modelling applications, these types of edits are among the hardest ones; they require high precision, but also a global awareness of the entire shape. Even in the deep learning era, obtaining manipulable representations that satisfy such requirements is an open problem posing significant constraints. In this work, we address this problem by defining a data‐driven model upon a family of linear operators (variants of the mesh Laplacian), whose spectra capture global and local geometric properties of the shape at hand. Modifications to these spectra are translated to semantically valid deformations of the corresponding surface. By explicitly decoupling the global from the local surface features, our pipeline allows to perform local edits while simultaneously maintaining a global stylistic coherence. We empirically demonstrate how our learning‐based model generalizes to shape representations not seen at training time, and we systematically analyze different choices of local operators over diverse shape categories.

A Massera theorem for asymptotic periodic solutions of periodic evolution equations

We present an analog of Massera Theorem for asymptotic periodic solutions of linear equations x′(t)=A(t)x(t)+f(t),t≥0(⁎), where the family of linear operators A(t) generates a 1-periodic process (U(t,s))t≥s≥0 in a Banach space X and f is asymptotic 1-periodic in the sense that limt→∞⁡(f(t+1)−f(t))=0. The main result says that if 1 is isolated in σ(U(1,0)) on the unit circle Γ, then (⁎) has an asymptotic 1-periodic mild solution if and only if it has an asymptotic mild solution that is bounded and uniformly continuous with precompact range. If 1∉σ(U(1,0))∩Γ, such an asymptotic 1-periodic mild solution always exists and unique within a function g(t) with limt→∞⁡g(t)=0. Our study relies on a spectral theory of functions on the half line and the evolution semigroups associated with linear equations. The obtained results seem to be new, even in the finite dimensional case.

Viability result for semilinear functional differential inclusions in Banach spaces

We show the existence result of a mild solution for a semilinear functional differential inclusion, with viability, governed by a family of linear operators. We consider the case when the constraint is moving.

Linear Independence of Time–Frequency Translates in $$L^p$$ Spaces

Fil: Antezana, Jorge Abel. Universidad Nacional de La Plata; Argentina. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Oficina de Coordinacion Administrativa Saavedra 15. Instituto Argentino de Matematica Alberto Calderon; Argentina

Model of interaction of pollution with aquatic technogenically loaded ecosystem

Scientific researches are devoted to the development of the theory of functional stability of ecosystems, as the stability of the functional of ecological safety. The conceptual (system of views of ensuring the ecosystem functional stability) and theoretical (the idea is comprehensively researched using scientifically-based approaches, methods, techniques, algorithms and mathematical models) of the theory of functional stability of ecosystems are offered. The theoretical bases of sustainable development of technogenically loaded ecosystems under conditions of synergism of components of ecological danger of different genesis are considered. On the example of the model of interaction of pollution of aquatic ecosystem its stability is investigated. The processes are described by Lot-Volterra type equations. This uses a modification of the first Lyapunov method, which is designed to study the stability of aquatic ecosystems of non-autonomous differential equations. For this purpose, a family of linear operators is constructed and the stability of systems of differential equations is determined by the signs of their logarithmic norms. Criteria for stability and asymptotic stability of fixed points by Lyapunov were obtained in the model of interaction of pollution with the aquatic ecosystem. The proposed method can be used to study a wide range of other ecosystems.

An Averaging Principle for the Time-Dependent Abstract Stochastic Evolution Equations with Infinite Delay and Wiener Process

In this paper, averaging principle for the time-dependent stochastic evolution equations (TDSEEs) with infinite delay is investigated. In proper non-Lipschitz conditions, we prove that the mild solution of the averaged stochastic evolution equations (ASEEs), governed by time-independent family of linear operators, converges to that of the original one in $$L^{2}$$ sense. At last, an application example is presented to prove the obtained theory.

Study on the q-analogue of a certain family of linear operators

Inthispaper, weintroducetheq-analogueofacertainfamilyoflinearoperatorsingeometricfunctiontheory. Our main purpose is to define some subclasses of analytic functions by means of the q-analogue of linear operators and investigate various inclusion relationships with integral preserving properties.

Existence and controllability results to second order neutral differential equation with non-instantaneous impulses

ABSTRACT In this paper, existence and uniqueness of the solutions of the second order neutral differential equation with non-instantaneous impulses in a Hilbert space X are studied. This is followed by a brief discussion on the exact and trajectory controllability. Further, the strongly continuous cosine family of linear operators and Banach fixed point theorem are used to establish the results. Finally, an example is given to illustrate the analytical findings.

Sequential evolution conformable differential equations of second order with nonlocal condition

In this paper, we investigate second order evolution differential equation in the frame of sequential conformable derivatives with nonlocal condition. First, we establish Duhamel’s formula in terms of a standard cosine family of linear operators. Then, we prove some results concerning the existence, uniqueness, stability, and regularity of mild solution concept. Moreover, we present a concrete application of the main results.

Periodicity of solutions to the Cauchy problem for nonautonomous impulsive delay evolution equations in Banach spaces

In this paper, we are concerned with the periodicity of solutions to the Cauchy problem for nonautonomous impulsive delay evolution equations with periodic inhomogenous terms in Banach spaces, where the operators in the linear part (possibly unbounded) depend on the time [Formula: see text] and generate an evolution family of linear operators. We first establish two new Gronwall–Bellman-type inequalities, and then prove a new and general existence theorem for periodic mild solutions to the nonautonomous impulsive delay evolution equations, which extends essentially some existing results even for the autonomous case as well as for the case when impulsive perturbations or delays are absent.

On Solvability of Boundary Value Problems for Kinetic Operator-Differential Equations

We study solvability of boundary value problems for the so-called kinetic operator-differential equations of the form B(t)ut−L(t)u = f, where L(t) and B(t) are families of linear operators defined in a complex Hilbert space E. We do not assume that the operator B is invertible and that the spectrum of the pencil L −λB is included into one of the half-planes Re λ a\({(a\in {\mathbb{R}})}\). Under certain conditions on the above operators, we prove several existence and uniqueness theorems and study smoothness questions in weighted Sobolev spaces for solutions.

Inclusion relationships for certain classes of analytic functions involving the Choi-Saigo-Srivastava operator

The purpose of the present paper is to investigate some inclusion properties of certain classes of analytic functions associated with a family of linear operators which are defined by means of the Hadamard product (or convolution). Some invariant properties under convolution are also considered for the classes presented here. The results presented here include several previous known results as their special cases.MSC:30C45.

Some inclusion relationships and integral-preserving properties of certain subclasses of p-valent meromorphic functions associated with a family of linear operator

Abstract By making use of a general linear operator we introduce several new subclasses of multvalent meromorphic functions and investigate various inclusion relationships. Several interesting integral-preversing properties are also discussed.

Argument estimates of certain meromorphically p-valent functions associated with a family of linear operator

Abstract Making use of linear operator we investigate some inclusion relationships and some argument properties of certain meromorphically p-valent functions.

On Certain Subclasses of Multivalent Functions Associated with a Family of Linear Operators

Making use of a linear operator Iλp(a,c), which is defined here by means of the Hadamard product (or convolution), we introduce some new subclasses of multivalent functions and investigate various inclusion properties of these subclasses. Some radius problems are also discussed.

On the differentiability of parametrized families of linear operators and the sensitivity of their stationary vectors

We investigate the differentiability of functions of stationary vectors associated with operator valued functions as well as the differentiability of the operator valued functions themselves. We display formulas connecting the derivatives of the parametric families of operators and vectors. The results are applied to the case of stochastic kernels.

Topologically transitive skew-products of operators

AbstractThe purpose of the present paper is to provide a link between skew-product systems and linear dynamics. In particular, we give a criterion for skew-products of linear operators to be topologically transitive. This is then applied to certain families of linear operators including scalar multiples of the backward shift, backward unilateral weighted shifts, composition, translation and differentiation operators. We also prove the existence of common hypercyclic vectors for certain families of skew-product systems.

Inclusion Properties for Certain Classes of Meromorphic Functions Associated with a Family of Linear Operators

The purpose of the present paper is to investigate some inclusion properties of certain classes of meromorphic functions associated with a family of linear operators, which are defined by means of the Hadamard product (or convolution). Some invariant properties under convolution are also considered for the classes presented here. The results presented here include several previous known results as their special cases.