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You searched for +publisher:"Universitat Politècnica de València" +contributor:("Fernandez Rosell, Carmen"). Showing records 1 – 3 of 3 total matches.

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Universitat Politècnica de València

1. Beltrán Meneu, María José. Operators on wighted spaces of holomorphic functions .

Degree: 2014, Universitat Politècnica de València

The Ph.D. Thesis ¿Operators on weighted spaces of holomorphic functions¿ presented here treats different areas of functional analysis such as spaces of holomorphic functions, infinite dimensional holomorphy and dynamics of operators. After a first chapter that introduces the notation, definitions and the basic results we will use throughout the thesis, the text is divided into two parts. A first one, consisting of Chapters 1 and 2, focused on a study of weighted (LB)-spaces of entire functions on Banach spaces, and a second one, corresponding to Chapters 3 and 4, where we consider differentiation and integration operators acting on different classes of weighted spaces of entire functions to study its dynamical behaviour. In what follows, we give a brief description of the different chapters: In Chapter 1, given a decreasing sequence of continuous radial weights on a Banach space X, we consider the weighted inductive limits of spaces of entire functions VH(X) and VH0(X). Weighted spaces of holomorphic functions appear naturally in the study of growth conditions of holomorphic functions and have been investigated by many authors since the work of Williams in 1967, Rubel and Shields in 1970 and Shields and Williams in 1971. We determine conditions on the family of weights to ensure that the corresponding weighted space is an algebra or has polynomial Schauder decompositions. We study Hörmander algebras of entire functions defined on a Banach space and we give a description of them in terms of sequence spaces. We also focus on algebra homomorphisms between these spaces and obtain a Banach-Stone type theorem for a particular decreasing family of weights. Finally, we study the spectra of these weighted algebras, endowing them with an analytic structure, and we prove that each function f ¿ VH(X) extends naturally to an analytic function defined on the spectrum. Given an algebra homomorphism, we also investigate how the mapping induced between the spectra acts on the corresponding analytic structures and we show how in this setting composition operators have a different behavior from that for holomorphic functions of bounded type. This research is related to recent work by Carando, García, Maestre and Sevilla-Peris. The results included in this chapter are published by Beltrán in [14]. Chapter 2 is devoted to study the predual of VH(X) in order to linearize this space of entire functions. We apply Mujica¿s completeness theorem for (LB)-spaces to find a predual and to prove that VH(X) is regular and complete. We also study conditions to ensure that the equality VH0(X) = VH(X) holds. At this point, we will see some differences between the finite and the infinite dimensional cases. Finally, we give conditions which ensure that a function f defined in a subset A of X, with values in another Banach space E, and admitting certain weak extensions in a space of holomorphic functions can be holomorphically extended in the corresponding space of vector-valued functions. Most of the results… Advisors/Committee Members: Bonet Solves, José Antonio (advisor), Fernandez Rosell, Carmen (advisor).

Subjects/Keywords: Weighted spaces of holomorphic functions; Hörmander algebras; Schauder decompositions; Spectra; Predual space; Linearization; Dynamics of operators; Hypercyclic; Chaotic; Power bounded and (uniformly) mean ergodic operators; Differentiation; Integration and Hardy operator.

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APA (6th Edition):

Beltrán Meneu, M. J. (2014). Operators on wighted spaces of holomorphic functions . (Doctoral Dissertation). Universitat Politècnica de València. Retrieved from http://hdl.handle.net/10251/36578

Chicago Manual of Style (16th Edition):

Beltrán Meneu, María José. “Operators on wighted spaces of holomorphic functions .” 2014. Doctoral Dissertation, Universitat Politècnica de València. Accessed August 22, 2019. http://hdl.handle.net/10251/36578.

MLA Handbook (7th Edition):

Beltrán Meneu, María José. “Operators on wighted spaces of holomorphic functions .” 2014. Web. 22 Aug 2019.

Vancouver:

Beltrán Meneu MJ. Operators on wighted spaces of holomorphic functions . [Internet] [Doctoral dissertation]. Universitat Politècnica de València; 2014. [cited 2019 Aug 22]. Available from: http://hdl.handle.net/10251/36578.

Council of Science Editors:

Beltrán Meneu MJ. Operators on wighted spaces of holomorphic functions . [Doctoral Dissertation]. Universitat Politècnica de València; 2014. Available from: http://hdl.handle.net/10251/36578

2. Ribera Puchades, Juan Miguel. Atomic decompositions and frames in Fréchet spaces and their duals .

Degree: 2015, Universitat Politècnica de València

[EN] The Ph.D. Thesis "Atomic decompositions and frames in Fréchet spaces and their duals" presented here treats different areas of functional analysis with applications. Schauder frames are used to represent an arbitrary element x of a function space E as a series expansion involving a fixed countable set {xj} of elements in that space such that the coefficients of the expansion of x depend in a linear and continuous way on x. Unlike Schauder bases, the expression of an element x in terms of the sequence {xj}, i.e. the reconstruction formula for x, is not necessarily unique. Atomic decompositions or Schauder frames are a less restrictive structure than bases, because a complemented subspace of a Banach space with basis has always a natural Schauder frame, that is obtained from the basis of the superspace. Even when the complemented subspace has a basis, there is not a systematic way to find it. Atomic decompositions appeared in applications to signal processing and sampling theory among other areas. Very recently, Pilipovic and Stoeva [55] studied series expansions in (countable) projective or inductive limits of Banach spaces. In this thesis we begin a systematic study of Schauder frames in locally convex spaces, but our main interest lies in Fréchet spaces and their duals. The main difference with respect to the concept considered in [55] is that our approach does not depend on a fixed representation of the Fréchet space as a projective limit of Banach spaces. The text is divided into two chapters and appendix that gives the notation, definitions and the basic results we will use throughout the thesis. The first one focuses on the relation between the properties of an existing Schauder frame in a Fréchet space E and the structure of the space. In the second chapter frames and Bessel sequences in Fréchet spaces and their duals are defined and studied. In what follows, we give a brief description of the different chapters: In Chapter 1, we study Schauder frames in Fréchet spaces and their duals, as well as perturbation results. We define shrinking and boundedly complete Schauder xviiframes on a locally convex space, study the duality of these two concepts and their relation with the reflexivity of the space. We characterize when an unconditional Schauder frame is shrinking or boundedly complete in terms of properties of the space. Several examples of concrete Schauder frames in function spaces are also presented. Most of the results included in this chapter are published by Bonet, Fernández, Galbis and Ribera in [13]. The second chapter of the thesis is devoted to study ¿-Bessel sequences, ¿-frames and frames with respect to ¿ in the dual of a Hausdorff locally convex space E, in particular for Fréchet spaces and complete (LB)-spaces E, with ¿ a sequence space. We investigate the relation of these concepts with representing systems in the sense of Kadets and Korobeinik [34] and with the Schauder frames, that were investigated in Chapter 1. The abstract results presented here, when applied to concrete spaces of… Advisors/Committee Members: Bonet Solves, José Antonio (advisor), Fernandez Rosell, Carmen (advisor), Galbis Verdu, Antonio (advisor).

Subjects/Keywords: Atomic decomposition; Schauder basis; Schauder frame; Shrinking frame; Boundedly complete frame; Frames; Representing systems; Su fficient and weakly su fficient sets; Reflexivity; Fréchet spaces; (LB)-spaces; Locally convex spaces

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APA (6th Edition):

Ribera Puchades, J. M. (2015). Atomic decompositions and frames in Fréchet spaces and their duals . (Doctoral Dissertation). Universitat Politècnica de València. Retrieved from http://hdl.handle.net/10251/49987

Chicago Manual of Style (16th Edition):

Ribera Puchades, Juan Miguel. “Atomic decompositions and frames in Fréchet spaces and their duals .” 2015. Doctoral Dissertation, Universitat Politècnica de València. Accessed August 22, 2019. http://hdl.handle.net/10251/49987.

MLA Handbook (7th Edition):

Ribera Puchades, Juan Miguel. “Atomic decompositions and frames in Fréchet spaces and their duals .” 2015. Web. 22 Aug 2019.

Vancouver:

Ribera Puchades JM. Atomic decompositions and frames in Fréchet spaces and their duals . [Internet] [Doctoral dissertation]. Universitat Politècnica de València; 2015. [cited 2019 Aug 22]. Available from: http://hdl.handle.net/10251/49987.

Council of Science Editors:

Ribera Puchades JM. Atomic decompositions and frames in Fréchet spaces and their duals . [Doctoral Dissertation]. Universitat Politècnica de València; 2015. Available from: http://hdl.handle.net/10251/49987


Universitat Politècnica de València

3. Jornet Casanova, David. Operadores Pseudodiferenciales en Clases no Casianalíticas de Tipo Beurling .

Degree: 2015, Universitat Politècnica de València

Los operadores pseudodiferenciales son generalizaciones de los operadores integrales singulares y de los operadores en derivadas parciales con coeficientes variables. A cada operador le corresponde un símbolo, que es una función infinitamente diferenciable y cuyas derivadas parciales cumplen ciertas estimaciones. El próposito es introducir estos operadores en el contexto de las clases no casianalíticas de tipo Beurling, clases que recientemente han recibido mucha atención, por ser más generales y unificar teorías anteriores. La tesis consta de tres capítulos. En el primero se definen los símbolos y operadors, se estudia entre qué espacios de funciones y ultradistribuciones actúan, se prueba que la clase es cerrada por trasposición y que los operadors son pseudolocales. También se dan ejemplos naturales de operadores en este contexto: operadores diferenciales cuyos coeficientes son funciones ultradiferencciables, los operadores regularizantes y los operadores ultradiferenciales en el sentido de Komatsu, y la convolución con una solución fundamental de un operador ultradiferencial elíptico. En el segundo capítulo se introduce el cálculo simbólico, cuyo objetivo es sustituir la teoría de los operadores por una algebraica de los correspondientes símbolos. El tercer capítulo está dedicado al estudio de la hipoelipticidad, concretamente de operadores en derivadas parciales de fuerza constante cuyos coeficientes están en una clase conveniente de funciones ultradiferenciables. Se prueba que en este contexto, la hipoelipticidad coincide con la hipoelipticidad homogénea, a priori más débil. También se establece una condición suficiente para la existencia de una paramétrix Advisors/Committee Members: Galbis Verdu, Antonio (advisor), Fernandez Rosell, Carmen (advisor), Martínez Jiménez, Félix (advisor).

Subjects/Keywords: Operadores Pseudodiferenciales; Clases no Casianalíticas; Tipo Beurling

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APA (6th Edition):

Jornet Casanova, D. (2015). Operadores Pseudodiferenciales en Clases no Casianalíticas de Tipo Beurling . (Doctoral Dissertation). Universitat Politècnica de València. Retrieved from http://hdl.handle.net/10251/54953

Chicago Manual of Style (16th Edition):

Jornet Casanova, David. “Operadores Pseudodiferenciales en Clases no Casianalíticas de Tipo Beurling .” 2015. Doctoral Dissertation, Universitat Politècnica de València. Accessed August 22, 2019. http://hdl.handle.net/10251/54953.

MLA Handbook (7th Edition):

Jornet Casanova, David. “Operadores Pseudodiferenciales en Clases no Casianalíticas de Tipo Beurling .” 2015. Web. 22 Aug 2019.

Vancouver:

Jornet Casanova D. Operadores Pseudodiferenciales en Clases no Casianalíticas de Tipo Beurling . [Internet] [Doctoral dissertation]. Universitat Politècnica de València; 2015. [cited 2019 Aug 22]. Available from: http://hdl.handle.net/10251/54953.

Council of Science Editors:

Jornet Casanova D. Operadores Pseudodiferenciales en Clases no Casianalíticas de Tipo Beurling . [Doctoral Dissertation]. Universitat Politècnica de València; 2015. Available from: http://hdl.handle.net/10251/54953

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