1,720,985 research outputs found
A characterization of a modulus of smoothness in multidimensional setting
No full textA classical result of approximation theory states that the modulus of smoothness of a function f (omega(f,delta)), defined by means of the variation functional, converges to 0 as delta tends to 0 from the right if and only if f is absolutely continuous. Such theorem is crucial in order to obtain results about convergence and order of approximation for linear and nonlinear integral operators in BV-spaces. It was an open problem to extend the above result to the setting of phi-variation in the multidimensional frame. In this paper, working with a concept of multidimensional phi-variation introduced in [Angeloni-Vinti, J. Math. Anal. Appl., 2009], we prove that an analogous characterization holds for the multidimensional phi-modulus of smoothness
Metodi di separazione in economia matematica: uguaglianza di Edgeworth, arbitraggio ed informazione asimmetrica
No full textIn questa nota si espongono i risultati principali ottenuti nella tesi di dottorato dal titolo "Separation methods in mathematical economics: Edgeworth Equivalence, arbitrage and asymmetric information". Nella tesi si affrontano due problemi nell’ambito della Teoria dell’Equilibrio Generale, la cui trattazione si basa su comuni strumenti matematici dell’analisi funzionale, in particolare sui teoremi di separazione. In particolare, nella prima parte si dimostra una versione dell'Uguaglianza di Edgeworth in assetto infinito-dimensionale, tramite un opportuno risultato di separazione in cui viene alleggerita l'ipotesi di convessità del sottoinsieme. Nella seconda parte si considera invece un modello di economia multiperiodo in presenza di asimmetria dell'informazione, studiando in particolare la condizione di non-arbitraggio e l'esistenza di equilibri finanziari
Convergence in variation for a homothetic modulus of smoothness in multidimensional setting
No full textIn order to get approximation results for linear and nonlinear convolution integral operators in -spaces, it is crucial to study convergence of the modulus of continuity. In the case of the modulus of continuity defined by means of the classical variation, it is well known that, if f is absolutely continuous, then the modulus of smoothness converges to 0, as tends to 0 from the right.
The purpose of this paper is to extend the above result to the frame of for the modulus of smoothness , where is the homothetic operator and is the multidimensional -variation introduced in [L. Angeloni-G. Vinti, "Convergence and rate of approximation for linear integral operators in BV^{\phi}-spaces in multidimensional setting", J. Math. Anal. Appl., 349(2) (2009), 317--334]
A New Concept of Multidimensional Variation in the Sense of Riesz and Applications to Integral Operators
No full textIn this paper we introduce and study a new multidimensional generalization in the sense of Tonelli of the Riesz–Medvedev φ-variation, proving in particular a multidimensional generalization of the Riesz–Medvedev theorem. We finally discuss an application of such concept of variation to some approximation problems: in particular, we obtain some estimates and convergence results by means of convolution integral operators in the space of functions of bounded φ-variation
Approximation in variation by homothetic operators in multidimensional setting
No full textThe aim of the present paper is to obtain convergence results and rates of approximation for a class of convolution integral operators of homothetic type in the space of functions of bounded phi-variation. In particular we work with the phi-variation in the sense of Musielak-Orlicz in multidimensional setting introduced in [L. Angeloni-G.Vinti, "Convergence and rate of approximation for linear integral operators in BV^phi-spaces in multidimensional setting", J. Math. Anal. Appl., 349 (2009), 317--334].The rate of approximation is also investigated, by means of suitable Lipschitz classes
Convergence in Variation and Rate of Approximation for Nonlinear Integral Operators of Convolution Type
No full textIn this paper we obtain estimates, convergence results and rate of approximation for functions belonging to BV−spaces (spaces of functions with bounded variation) by means of nonlinear convolution integral operators. We treat both the periodic and the non-periodic case using, respectively, the classical Jordan variation and the multidimensional variation in the sense of Tonelli
Errata Corrige to: "Approximation by means of Nonlinear Integral Operators in the Space of Functions with Bounded phi-Variation"
No full textIn this Errata Corrige the authors want to point out that a term in the proof of one of the results in the original paper has to be estimated in a different way. In order to do this a new condition on kernel functions (K_w.3'), which is a light modification of the original condition (K_w.3) is proposed and discussed
A sufficient condition for the convergence of a certain modulus of smoothness in multidimensional setting
No full textIn this paper we prove a convergence result for the modulus of smoothness in the frame of , namely the space of functions of bounded variation on equipped with the logarithmic measure. In particular we prove that, similarly to what happens in the classical case of the Jordan variation,
for some , if is absolutely continuous. Here , where , , is the dilation operator and denotes a new concept of multivariate variation in the sense of Tonelli
Variation and approximation for Mellin-type operators
No full textMellin analysis is of extreme importance in approximation theory, also for its wide applications: among them, for example, it is connected with problems of Signal Analysis, such as the Exponential Sampling. Here we study a family of Mellin-type integral operators defined as (T_w f)({\tt s})=\int_{\R_+^N} K_w({\tt t}) f({\tt st}){\,d{\tt t} \over \langle{\tt t}\rangle}, \ {\tt s}\in \R_+^N,\ w>0,\eqno \rm{(I)} where are (essentially) bounded approximate identities, , and is a function of bounded variation. We use a new concept of multidimensional variation inspired by the Tonelli approach, which preserves some of the main properties of the classical variation. For the family of operators (I), besides several estimates and a result of approximation for the modulus of smoothness, the main convergence result that we obtain proves that for some , provided that is absolutely continuous. Moreover, the problem of the rate of approximation is studied, taking also into consideration the particular case of Fej\'er-type kernels
Rate of approximation for nonlinear integral operators with application to signal processing
No full textWe study the problem of the order of approximation in modular spaces for a family of nonlinear integral operators of the form. The general setting of modular spaces allows us to obtain, in particular, rate of approximation in L^p spaces and in Orlicz-type spaces. Furthermore, the general class of operators that we study contains, as particular cases, some classical families of integral operators well known in approximation theory, such as the classical convolution integral operators, the Mellin convolution integral operators and the sampling-type operators in their nonlinear form. Our approach, in the framework of modular spaces, is mainly based on the introduction of a suitable Lipschitz class and of a condition on a family of measures which is linked with the modulars involved and which is always fulfilled in classical and Musielak-Orlicz spaces
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