Displaying similar documents to “On embeddings of function classes defined by constructive characteristics”

Pointwise inequalities and approximation in fractional Sobolev spaces

David Swanson (2002)

Studia Mathematica

Similarity:

We prove that a function belonging to a fractional Sobolev space L α , p ( ) may be approximated in capacity and norm by smooth functions belonging to C m , λ ( ) , 0 < m + λ < α. Our results generalize and extend those of [12], [4], [14], and [11].

Lebesgue type points in strong (C,α) approximation of Fourier series

Włodzimierz Łenski, Bogdan Roszak (2011)

Banach Center Publications

Similarity:

We present an estimation of the H k , k r q , α f and H λ , u ϕ , α f means as approximation versions of the Totik type generalization (see [5], [6]) of the result of G. H. Hardy, J. E. Littlewood. Some corollaries on the norm approximation are also given.

Approximation polynômiale dans des classes de jets

Moulay Taïb Belghiti, Boutayeb El Ammari, Laurent P. Gendre (2015)

Banach Center Publications

Similarity:

In this paper we obtain results on approximation, in the multidimensional complex case, of functions from ( K ) by complex polynomials. In particular, we generalize the results of Pawłucki and Pleśniak (1986) for the real case and of Siciak (1993) in the case of one complex variable. Furthermore, we extend the results of Baouendi and Goulaouic (1971) who obtained the order of approximation in the case of Gevrey classes over real compacts with smooth analytic boundary and we present the orders...

The degree of approximation by Hausdorff means of a conjugate Fourier series

Sergiusz Kęska (2016)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

Similarity:

The purpose of this paper is to analyze the degree of approximation of a function f ¯ that is a conjugate of a function f belonging to the Lipschitz class by Hausdorff means of a conjugate series of the Fourier series.

Limiting behaviour of intrinsic seminorms in fractional order Sobolev spaces

Rémi Arcangéli, Juan José Torrens (2013)

Studia Mathematica

Similarity:

We collect and extend results on the limit of σ 1 - k ( 1 - σ ) k | v | l + σ , p , Ω p as σ → 0⁺ or σ → 1¯, where Ω is ℝⁿ or a smooth bounded domain, k ∈ 0,1, l ∈ ℕ, p ∈ [1,∞), and | · | l + σ , p , Ω is the intrinsic seminorm of order l+σ in the Sobolev space W l + σ , p ( Ω ) . In general, the above limit is equal to c [ v ] p , where c and [·] are, respectively, a constant and a seminorm that we explicitly provide. The particular case p = 2 for Ω = ℝⁿ is also examined and the results are then proved by using the Fourier transform.

On subextension and approximation of plurisubharmonic functions with given boundary values

Hichame Amal (2014)

Annales Polonici Mathematici

Similarity:

Our aim in this article is the study of subextension and approximation of plurisubharmonic functions in χ ( Ω , H ) , the class of functions with finite χ-energy and given boundary values. We show that, under certain conditions, one can approximate any function in χ ( Ω , H ) by an increasing sequence of plurisubharmonic functions defined on strictly larger domains.

Whitney type inequality, pointwise version

Yu. A. Brudnyi, I. E. Gopengauz (2013)

Studia Mathematica

Similarity:

The main result of the paper estimates the asymptotic behavior of local polynomial approximation for L p functions at a point via the behavior of μ-differences, a generalization of the kth difference. The result is applied to prove several new and extend classical results on pointwise differentiability of L p functions including Marcinkiewicz-Zygmund’s and M. Weiss’ theorems. In particular, we present a solution of the problem posed in the 30s by Marcinkiewicz and Zygmund.

Fractional integral operators on B p , λ with Morrey-Campanato norms

Katsuo Matsuoka, Eiichi Nakai (2011)

Banach Center Publications

Similarity:

We introduce function spaces B p , λ with Morrey-Campanato norms, which unify B p , λ , C M O p , λ and Morrey-Campanato spaces, and prove the boundedness of the fractional integral operator I α on these spaces.

Some duality results on bounded approximation properties of pairs

Eve Oja, Silja Treialt (2013)

Studia Mathematica

Similarity:

The main result is as follows. Let X be a Banach space and let Y be a closed subspace of X. Assume that the pair ( X * , Y ) has the λ-bounded approximation property. Then there exists a net ( S α ) of finite-rank operators on X such that S α ( Y ) Y and | | S α | | λ for all α, and ( S α ) and ( S * α ) converge pointwise to the identity operators on X and X*, respectively. This means that the pair (X,Y) has the λ-bounded duality approximation property.

Convergence of greedy approximation II. The trigonometric system

S. V. Konyagin, V. N. Temlyakov (2003)

Studia Mathematica

Similarity:

We study the following nonlinear method of approximation by trigonometric polynomials. For a periodic function f we take as an approximant a trigonometric polynomial of the form G ( f ) : = k Λ f ̂ ( k ) e i ( k , x ) , where Λ d is a set of cardinality m containing the indices of the m largest (in absolute value) Fourier coefficients f̂(k) of the function f. Note that Gₘ(f) gives the best m-term approximant in the L₂-norm, and therefore, for each f ∈ L₂, ||f-Gₘ(f)||₂ → 0 as m → ∞. It is known from previous results that in...

On the approximation of real continuous functions by series of solutions of a single system of partial differential equations

Carsten Elsner (2006)

Colloquium Mathematicae

Similarity:

We prove the existence of an effectively computable integer polynomial P(x,t₀,...,t₅) having the following property. Every continuous function f : s can be approximated with arbitrary accuracy by an infinite sum r = 1 H r ( x , . . . , x s ) C ( s ) of analytic functions H r , each solving the same system of universal partial differential equations, namely P ( x σ ; H r , H r / x σ , . . . , H r / x σ ) = 0 (σ = 1,..., s).

On Sobolev spaces of fractional order and ε-families of operators on spaces of homogeneous type

A. Gatto, Stephen Vági (1999)

Studia Mathematica

Similarity:

We introduce Sobolev spaces L α p for 1 < p < ∞ and small positive α on spaces of homogeneous type as the classes of functions f in L p with fractional derivative of order α, D α f , as introduced in [2], in L p . We show that for small α, L α p coincides with the continuous version of the Triebel-Lizorkin space F p α , 2 as defined by Y. S. Han and E. T. Sawyer in [4]. To prove this result we give a more general definition of ε-families of operators on spaces of homogeneous type, in which the identity...

A remark on the approximation theorems of Whitney and Carleman-Scheinberg

Michal Johanis (2015)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We show that a C k -smooth mapping on an open subset of n , k { 0 , } , can be approximated in a fine topology and together with its derivatives by a restriction of a holomorphic mapping with explicitly described domain. As a corollary we obtain a generalisation of the Carleman-Scheinberg theorem on approximation by entire functions.

Density estimation via best L 2 -approximation on classes of step functions

Dietmar Ferger, John Venz (2017)

Kybernetika

Similarity:

We establish consistent estimators of jump positions and jump altitudes of a multi-level step function that is the best L 2 -approximation of a probability density function f . If f itself is a step-function the number of jumps may be unknown.

New characterizations and applications of inhomogeneous Besov and Triebel-Lizorkin spaces on homogeneous type spaces and fractals

Yongsheng Han, Dachun Yang

Similarity:

Let d > 0 and θ ∈ (0,1]. We consider homogeneous type spaces, ( X , ϱ , μ ) d , θ , which are variants of the well known homogeneous type spaces in the sense of Coifman and Weiss. We introduce fractional integrals and derivatives, and prove that the Besov spaces B p q s ( X ) and Triebel-Lizorkin spaces F p q s ( X ) have the lifting properties for |s| < θ. Moreover, we give explicit representations for the inverses of these fractional integrals and derivatives. By using these representations, we prove that the fractional...

Rational approximation to real points on conics

Damien Roy (2013)

Annales de l’institut Fourier

Similarity:

A point ( ξ 1 , ξ 2 ) with coordinates in a subfield of of transcendence degree one over , with 1 , ξ 1 , ξ 2 linearly independent over , may have a uniform exponent of approximation by elements of 2 that is strictly larger than the lower bound 1 / 2 given by Dirichlet’s box principle. This appeared as a surprise, in connection to work of Davenport and Schmidt, for points of the parabola { ( ξ , ξ 2 ) ; ξ } . The goal of this paper is to show that this phenomenon extends to all real conics defined over , and that the largest...

Embeddings of Besov spaces of logarithmic smoothness

Fernando Cobos, Óscar Domínguez (2014)

Studia Mathematica

Similarity:

This paper deals with Besov spaces of logarithmic smoothness B p , r 0 , b formed by periodic functions. We study embeddings of B p , r 0 , b into Lorentz-Zygmund spaces L p , q ( l o g L ) β . Our techniques rely on the approximation structure of B p , r 0 , b , Nikol’skiĭ type inequalities, extrapolation properties of L p , q ( l o g L ) β and interpolation.

A uniform dimension result for two-dimensional fractional multiplicative processes

Xiong Jin (2014)

Annales de l'I.H.P. Probabilités et statistiques

Similarity:

Given a two-dimensional fractional multiplicative process ( F t ) t [ 0 , 1 ] determined by two Hurst exponents H 1 and H 2 , we show that there is an associated uniform Hausdorff dimension result for the images of subsets of [ 0 , 1 ] by F if and only if H 1 = H 2 .

Generalized α-variation and Lebesgue equivalence to differentiable functions

Jakub Duda (2009)

Fundamenta Mathematicae

Similarity:

We find conditions on a real function f:[a,b] → ℝ equivalent to being Lebesgue equivalent to an n-times differentiable function (n ≥ 2); a simple solution in the case n = 2 appeared in an earlier paper. For that purpose, we introduce the notions of C B V G 1 / n and S B V G 1 / n functions, which play analogous rôles for the nth order differentiability to the classical notion of a VBG⁎ function for the first order differentiability, and the classes C B V 1 / n and S B V 1 / n (introduced by Preiss and Laczkovich) for Cⁿ smoothness....

Density of some sequences modulo 1

Artūras Dubickas (2012)

Colloquium Mathematicae

Similarity:

Recently, Cilleruelo, Kumchev, Luca, Rué and Shparlinski proved that for each integer a ≥ 2 the sequence of fractional parts a / n n = 1 is everywhere dense in the interval [0,1]. We prove a similar result for all Pisot numbers and Salem numbers α and show that for each c > 0 and each sufficiently large N, every subinterval of [0,1] of length c N - 0 . 475 contains at least one fractional part Q(αⁿ)/n, where Q is a nonconstant polynomial in ℤ[z] and n is an integer satisfying 1 ≤ n ≤ N.

Generalized fractional integrals on central Morrey spaces and generalized λ-CMO spaces

Katsuo Matsuoka (2014)

Banach Center Publications

Similarity:

We introduce the generalized fractional integrals I ̃ α , d and prove the strong and weak boundedness of I ̃ α , d on the central Morrey spaces B p , λ ( ) . In order to show the boundedness, the generalized λ-central mean oscillation spaces Λ p , λ ( d ) ( ) and the generalized weak λ-central mean oscillation spaces W Λ p , λ ( d ) ( ) play an important role.