11 research outputs found

    Numerical solution of matrix interpolation problems

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    Intertwining operators

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    Norm estimates for functions of semigroups of operators

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    Topics in the theory of nonself-adjoint operator algebras

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    Function spaces defined by means of oscillation, with application

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    In the mathematical literature, a plethora of different meanings and formal definitions have been associated to the word "oscillation". In this text we will explore some of the function spaces defined by means of oscillation, in many different senses of the word, fitting into two modes: spaces in which oscillation is bounded and spaces in which oscillation is vanishing, i.e. arbitrarily small when measured on a sufficiently small set. This general framework will be made precise in a diversity of ways. The outline of the thesis is the following. In the first chapter a very large space of functions introduced by Brezis, Bourgain and Mironescu in 2015 and often denoted as BB is introduced. In Chapter 2 we explore the space of Lipschitz functions, in the most general setting of an arbitrary compact metric space and together with other function spaces from the family of Holder spaces. The last section of the Chapter 2 is devoted to some results obtained in the field of Optimal Control Theory. In Chapter 33 we introduce Orlicz spaces for any choice of a Young function Ψ\Psi and the closure of L∞L^\infty in LΨL^\Psi, also known as the Morse space MΨM^\Psi. We individuate a large subfamily of Orlicz spaces for which (LΨ,MΨ)(L^\Psi,M^\Psi) fits into a mathematical framework by K.M. Perfekt, deriving many functional properties of the couple.\\ In particular, in the last section of this chapter, we discuss some applications to the regularity of minima of some functionals in the calculus of variations. Chapters 4 and 5 are dedicated to the spaces BMOBMO and VMOVMO and their respective subcones BLOBLO and VLOVLO, concluding the text with discussion of what are arguably the most natural "children" of the very large space BB discussed at the beginning

    Acta Scientiarum Mathematicarum : Tomus 53. Fasc. 1-2.

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    Acta Scientiarum Mathematicarum : Tomus 42. Fasc. 1-2.

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    Acta Scientiarum Mathematicarum : Tomus 43. Fasc. 1-2.

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    Harmonic approximation and Sarason's-type theorem

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    Hansen W, Netuka I. Harmonic approximation and Sarason's-type theorem. Journal of Approximation Theory. 2003;120(1):183-190.In this paper uniform approximation of bounded harmonic functions on an arbitrary open set in Euclidean space by harmonic functions arising as solutions of the classical or generalized Dirichlet problem is studied. In particular, an analogue of Sarason's H-infinity + C theorem (known from the theory of algebras of analytic functions) is established for harmonic functions. (C) 2002 Elsevier Science (USA). All rights reserved
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