Abstract: We introduce several notions of **linear** dynamics for multivalued **linear** **operators** (MLO’s) between separable Fréchet spaces, such as hypercyclicity, topological transitivity, topologically mixing property, and Devaney chaos. We also consider the case of disjointness, in which any of these properties are simultaneously satisfied by several **operators**. We revisit some sufficient well-known computable criteria for determining those properties. The analysis of the dynamics of extensions of **linear** **operators** to MLO’s is also considered.

11 Lee mas

We will not use the theory of C*-algebras in general, in fact we will use just the C*- algebras shown in example 2.4. We will define an operator f (T) for any continuous function f using an homomorphism between C*-algebras. We will construct a map from the set of all continuous functions on a compact set to the set of all bounded **linear** **operators** on a Hilbert space. We will construct this homomorphism as an extension of the definition 2.1 using the Weierstrass Theorem.

64 Lee mas

ABSTRAC T . In [ Na-4 } we presen ted an abstract framework in which the spec trum of a **linear** operator can be compu ted through a characteristic equation. In tIle present note this is combined with the Perron - Frobenius spectral theory for positive **operators** in order to obtain simple stabili ty criteria for the solu tions of

8 Lee mas

This method is an application of Hilbert Space methods to the solution of integral equations, where the goal is again to best approximate the exact solution. The criterion of best appr[r]

8 Lee mas

R (T ) + N (T d ) is of ﬁnite codimension. Moreover, if T is B-Fredholm then ind(T ) = dim N (T ) ∩R (T d ) − codim R (T) + N (T d ). Based on this characterization of B-Fredholm bounded **operators**, we introduce the class of B-Fredholm closed **linear** **operators** acting on a Hilbert space H and study its properties. Mainly, we prove that an operator T ∈ C (H ) densely deﬁned on H is a B-Fredholm operator if and only if T = T 0 ⊕ T 1 , where T 0 is a

12 Lee mas

Throughout this paper let B(H), F(H), K(H), denote, respectively, the algebra of bounded **linear** **operators**, the ideal of finite rank **operators** and the ideal of compact **operators** acting on an infinite dimensional separable Hilbert space H. If T ∈ B(H) we shall write ker(T ) and R(T ) (or ran(T )) for the null space and range of T , respectively. Also, let α(T ) := dim ker(T ), β(T ) := co dim R(T ), and let σ(T ), σ a (T ), σ p (T ) denote the spectrum, approximate point spectrum and point

10 Lee mas

Once the basic properties are established, the second step was to study the boundedness of the Hardy–Littlewood maximal operator and the fractional Hardy– Littlewood maximal operator on the variable Lebesgue spaces; see Theorem 1 and Theorem 2 below and references therein. With these tools one can then study other **operators** such as convolution **operators**, singular integral **operators**, fractional type **operators**, and Riesz potentials. Several results about these **operators** can be found in the papers [1, 2, 7, 10, 17, 18, 20, 21].

16 Lee mas

It is well known that B´ ezier curves are the parametric curves used in computer graphics and designs. In vector graphics they are used to model smooth curves and also used in animation designs. Zeng and Piriou [18] pioneered the study of B´ ezier variants of Bernstein **operators**. The papers by other researchers (e.g., [3, 5, 8, 13, 17]) motivate us to study further in this direction.

16 Lee mas

This paper is a summary of the talk held by the author in the conference “X Encuentro de Analistas A. Calderón”, that was celebrated in La Falda, Córdoba, in Argentina, in September 2010. Our purpose is to present a survey about Hardy spaces associated with semigroups of **operators**. Of course it is not possible to be ex- haustive. There exist monographs about this topic (see [25], [43], and [50], amongst others) and almost every day a paper where Hardy spaces appear is written. This shows the great importance of the Hardy spaces.

22 Lee mas

El servicio técnico de **Linear** proporciona soporte telefónico temprano por la mañana y fuera del horario habitual para su línea de productos en expansión. Los ingenieros de aplicaciones están listos para ayudarlo con las preguntas técnicas respecto de todos los productos **Linear** y de la instalación del equipo, la programación, el diseño del sistema, la solución de problemas y la compatibilidad entre sistemas.

10 Lee mas

Note that e(F, V) is a non-**linear** function of F . Hence, for the problems described in the introduction, what we want is to minimize e over all possible bundles of subspaces. To show that all these problems have indeed a (constructive) solution, we need some definitions (for details we refer the reader to [5]).

9 Lee mas

2. In general I try to work problems in class that are different from my notes. However, with a **Linear** Algebra course while I can make up the problems off the top of my head there is no guarantee that they will work out nicely or the way I want them to. So, because of that my class work will tend to follow these notes fairly close as far as worked problems go. With that being said I will, on occasion, work problems off the top of my head when I can to provide more examples than just those in my notes. Also, I often don’t have time in class to work all of the problems in the notes and so you will find that some sections contain problems that weren’t worked in class due to time restrictions. 3. Sometimes questions in class will lead down paths that are not covered here. I try to

Mostrar más
343 Lee mas

Weighted ordered weighted averaging (WOWA) and semiuninorm-based ordered weighted averaging (SUOWA) **operators** are two families of aggre- gation functions that simultaneously generalize weighted means and OWA **operators**. Both families can be obtained by using the Choquet integral with respect to normalized capacities. Therefore, they are continuous, monotonic, idempotent, compensative and homogeneous of degree 1 func- tions. Although both families fulfill good properties, there are situations where their behavior is quite different. The aim of this paper is to analyze both families of functions regarding some simple cases of weighting vec- tors, the capacities from which they are building, the weights affecting the components of each vector, and the values they return.

Mostrar más
26 Lee mas

Abstract. This paper is essentially the second author’s lecture at the CIMPA– UNESCO Argentina School 2008, Real Analysis and its Applications. It sum- marises large parts of the three authors’ paper [MSV]. Only one proof is given. In the setting of a Euclidean space, we consider **operators** defined and uniformly bounded on atoms of a Hardy space H p . The question discussed is

8 Lee mas

Although both families of **operators** allow solving a wide range of problems, both weightings are necessary in some contexts. Some examples of these situations have been given by several authors (see, for instance, Torra [2–4], Torra and Godo [5, pages 160-161], Torra and Narukawa [6, pages 150- 151], Roy [7], Yager and Alajlan [8], and Llamazares [9] and the references therein) in fields as diverse as robotics, vision, fuzzy logic controllers, constraint satisfaction prob- lems, scheduling, multicriteria aggregation problems, and decision-making.

12 Lee mas

El avance m´ as sobresaliente en este problema se lo debemos a Hironaka, que en 1964 prob´ o que cualquier variedad definida sobre un cuerpo de caracter´ıstica cero admite una resoluci´ [r]

175 Lee mas

In this paper, we introduce a more general set of operators on M than were given by Taká cˇ, and we study, among other properties, the conditions required to satisfy the axioms of the [r]

17 Lee mas

Due to the fact that the calculation of deficiency spaces is difficult for dimension greater than one, another approach to find self-adjoint extensions was proposed by Friedrichs, Kato and oth- ers. This approach considers quadratic forms associated to symmetric **operators**. If a quadratic form is closable it is related to a unique self-adjoint operator. We arrived at Kato’s represen- tation theorem, which allows one to obtain self-adjoint extensions of symmetric, semi-bounded **operators**.

42 Lee mas

In this expository article we want to recount a few recent results in the study of certain multilinear **operators**. Multilinear harmonic analysis is an active area of research that is still developing. We will limit ourselves to results that are, in a way, natural multilinear versions of well-known and powerful theorems in the study of **linear** singular integrals of Calder´ on-Zygmund type. These new results only arise after many important progresses have been done in related topics and by numerous authors. This presentation is far from being exhaustive in the sense that, for reasons of space, we will not be able to describe all existing contributions in multilinear analysis but only those most closely related to **operators** with variable coefficients. We will concentrate on some progresses done on a series of collabora- tions and some topics presented by the author at the 2008 CIMPA-UNESCO School on Real Analysis and its Applications. One of the focus points of the conference was precisely new aspects of the Calder´ on-Zygmund theory. We will assume that the interested reader has some familiarity with basic results about **linear** Calder´ on- Zygmund **operators** and **linear** pseudodifferntial **operators**, but refer to the book by Stein [65] for a comprehensive introduction. Also for brevity, we will not present the theorems in their greatest generality, but with hypotheses that simplify the narrative and still encapsulate the main mathematical aspects involved.

Mostrar más
18 Lee mas

They allow the formation of diffuser continuous lines, with active and inactive areas, without breaking the uniformity of the whole.. They are suitable both for supply and return.[r]

10 Lee mas