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Approximation in Hardy Spaces [PDF]
, 1992 Since the transfer function (or matrix) of a stable linear system is analytic in |z| ≥ 1, the transformation z → z −1 guarantees its analyticity in the unit disk |z| ≤ 1. In this chapter we will study approximation by polynomials and “stable” rational functions in |z| ≤ 1, using the Hardy spaces H 2 and norms. Here, due to the reciprocal transformation,
Guanrong Chen, Charles K. Chui
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Introducing the Polylogarithmic Hardy Space
, 2015In this paper we investigate the reproducing kernel Hilbert space where the polylogarithm appears as the kernel function. This investigation begins with the properties of functions in this space, and here a connection to the classical Hardy space is ...
Joel A. Rosenfeld
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Invariant Metrics for the Quaternionic Hardy Space
, 2013We find Riemannian metrics on the unit ball of the quaternions, which are naturally associated with reproducing kernel Hilbert spaces. We study the metric arising from the Hardy space in detail. We show that, in contrast to the one-complex variable case,
N. Arcozzi, G. Sarfatti
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Quaestiones Mathematicae, 2004
We summarize the results on multipliers from Hp to lq for various p and q. In some instances we provide proofs which are different from the ones in the literature. On other occasions we are able to improve results of other authors, or provide an unified treatment that does not appear in the literature.Mathematics Subject Classification (2000): 30D ...
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We summarize the results on multipliers from Hp to lq for various p and q. In some instances we provide proofs which are different from the ones in the literature. On other occasions we are able to improve results of other authors, or provide an unified treatment that does not appear in the literature.Mathematics Subject Classification (2000): 30D ...
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1992
In Chapter 1 we defined the Poisson integral of a function f ∈ C(S) to be the function P[f] defined on B by $$P\left[ f \right](x) = \int_S {P\left( {x,\zeta } \right)f} \left( \zeta \right)d\sigma \left( \zeta \right)$$ (6.1) .
Wade Ramey +2 more
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In Chapter 1 we defined the Poisson integral of a function f ∈ C(S) to be the function P[f] defined on B by $$P\left[ f \right](x) = \int_S {P\left( {x,\zeta } \right)f} \left( \zeta \right)d\sigma \left( \zeta \right)$$ (6.1) .
Wade Ramey +2 more
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Parametrized Area Integrals on Hardy Spaces and Weak Hardy Spaces
Acta Mathematica Sinica, English Series, 2007In this paper, the authors prove that if Ω satisfies a class of the integral Dini condition, then the parametrized area integral $$ \mu ^{\rho }_{{\Omega ,S}} $$ is a bounded operator from the Hardy space H 1(ℝ n
Shanzhen Lu, Yong Ding, Qingying Xue
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Annali di Matematica Pura ed Applicata, 1984
We prove direct and converse theorems of approximation for distributions in the Hardy spaces Hp ...
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We prove direct and converse theorems of approximation for distributions in the Hardy spaces Hp ...
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Indiana University Mathematics Journal, 2014
We develop the theory of variable exponent Hardy spaces Hp(·). We give equivalent definitions in terms of maximal operators that are analogous to the classical theory. We also show that Hp(·) functions have an atomic decomposition including a “finite” decomposition; this decomposition is more like the decomposition for weighted Hardy spaces due to ...
David Cruz-Uribe, Daniel Wang
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We develop the theory of variable exponent Hardy spaces Hp(·). We give equivalent definitions in terms of maximal operators that are analogous to the classical theory. We also show that Hp(·) functions have an atomic decomposition including a “finite” decomposition; this decomposition is more like the decomposition for weighted Hardy spaces due to ...
David Cruz-Uribe, Daniel Wang
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, 2011
We introduce connections between the Cuntz relations and the Hardy space H 2 of the open unit disk \(\mathbb{D}\). We then use them to solve a new kind of multipoint interpolation problem in H 2, where, for instance, only a linear combination of the ...
D. Alpay +3 more
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We introduce connections between the Cuntz relations and the Hardy space H 2 of the open unit disk \(\mathbb{D}\). We then use them to solve a new kind of multipoint interpolation problem in H 2, where, for instance, only a linear combination of the ...
D. Alpay +3 more
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1998
In this chapter we study various properties of the spacesH 1 H 2 andH ∞in preparation for our study of Toeplitz operators in the following chapter. Due to the availability of several excellent accounts of this subject (see Notes), we do not attempt a comprehensive treatment and proceed in the main using the techniques which we have already introduced.
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In this chapter we study various properties of the spacesH 1 H 2 andH ∞in preparation for our study of Toeplitz operators in the following chapter. Due to the availability of several excellent accounts of this subject (see Notes), we do not attempt a comprehensive treatment and proceed in the main using the techniques which we have already introduced.
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