"Hardy class" redirects here. For the warships, see Hardy class destroyer.
In complex analysis, the Hardy spaces (or Hardy classes) Hp are certain spaces of holomorphic functions on the unit disk or upper half plane. They were introduced by Frigyes Riesz (Riesz 1923), who named them after G. H. Hardy, because of the paper (Hardy 1915). In real analysis Hardy spaces are certain spaces of distributions on the real line, which are (in the sense of distributions) boundary values of the holomorphic functions of the complex Hardy spaces, and are related to the Lp spaces of functional analysis. For 1 ≤ p < ∞ these real Hardy spaces Hp are certain subsets of Lp, while for p < 1 the Lp spaces have some undesirable properties, and the Hardy spaces are much better behaved.
There are also higher-dimensional generalizations, consisting of certain holomorphic functions on tube domains in the complex case, or certain spaces of distributions on Rn in the real case.
Hardy spaces have a number of applications in mathematical analysis itself, as well as in control theory (such as H∞ methods) and in scattering theory.
In complex analysis, the Hardyspaces (or Hardy classes) Hp are certain spaces of holomorphic functions on the unit disk or upper half plane. They were...
generalized functions, and Hardyspaces of holomorphic functions. Geometric intuition plays an important role in many aspects of Hilbert space theory. Exact analogs...
become the classical Cauchy transform, the orthogonal projection onto Hardyspace, and the Hilbert transform a real orthogonal linear complex structure...
indistinguishable. Bochner space – Type of topological space Orlicz space – Type of function spaceHardyspace – Concept within complex analysis Riesz–Thorin theorem –...
topology all functions, space of pointwise convergence Hardyspace Hölder space Càdlàg functions, also known as the Skorokhod space Lip 0 ( R ) {\displaystyle...
is the compression of a multiplication operator on the circle to the Hardyspace. Let S 1 {\displaystyle S^{1}} be the complex unit circle, with the standard...
Thomas Hardy OM (2 June 1840 – 11 January 1928) was an English novelist and poet. A Victorian realist in the tradition of George Eliot, he was influenced...
{\displaystyle L^{2}(\mathbb {R} ).} The operator U carries the Hardyspace H2(T) onto the Hardyspace H 2 ( R ) {\displaystyle H^{2}(\mathbb {R} )} . Bedrosian's...
Hardyspace, H p , {\displaystyle H^{p},} and in particular, ‖ u ‖ H p = ‖ f ‖ L p {\displaystyle \|u\|_{H^{p}}=\|f\|_{L^{p}}} Thus, again, the Hardy...
versa. The space of progressive functions is sometimes denoted H + 2 ( R ) {\displaystyle H_{+}^{2}(R)} , which is known as the Hardyspace of the upper...
a Hardyspace with square norm. It is a subspace of L2 space, and is thus a Hilbert space. In particular, it is a reproducing kernel Hilbert space. In...
The space of functions of bounded mean oscillation (BMO), is a function space that, in some precise sense, plays the same role in the theory of Hardy spaces...
spaces in abstract mathematics, by Wikipedia page. Banach space Besov space Bochner space Dual space Euclidean space Fock space Fréchet spaceHardy space...
followed by projection onto the Hardyspace) has inspired the study of similar questions on other spaces, such as the Bergman space. The theory of operator algebras...
{G}}} are some unspecified function spaces, such as Hardyspace, Lp space, Sobolev space, or, more vaguely, the space of holomorphic functions. List of...
various function spaces of holomorphic functions on the disk. These spaces include the Hardyspaces, the Bergman spaces and Dirichlet space. Let h be a holomorphic...
products were introduced by Wilhelm Blaschke (1915). They are related to Hardyspaces. A sequence of points ( a n ) {\displaystyle (a_{n})} inside the unit...
which are compressions of multiplication operators on the circle to the Hardyspace. A multiplication operator T f {\displaystyle T_{f}} on L 2 ( X ) {\displaystyle...
of several real variables (see multidimensional Laplace transform). Hardyspaces on tubes can be defined in a manner in which a version of the Paley–Wiener...
Hardy, Hardy, and Krugman: p. 11. Hardy, Hardy, and Krugman: p. 12. Hardy, Hardy, and Krugman: p. 45. Hardy, Hardy, and Krugman: p. 46. Hardy, Hardy,...
The Hardys, also known as the Hardy Boyz, are an American professional wrestling tag team consisting of brothers Matt Hardy and Jeff Hardy. They first...
Fréchet space – A locally convex topological vector space that is also a complete metric spaceHardyspace – Concept within complex analysis Hilbert space –...
This is a list of all Hardy Boys books published, by series. In 1979, the Hardy Boys books began to be published by Wanderer Books Simon & Schuster in...
2017) was an American mathematician whose research topics included Hardyspace theory and VMO. As a professor at the University of California, Berkeley...
D}{\frac {f(\zeta )\,d\zeta }{\zeta -z}}.} Moreover, let H2(∂D) be the Hardyspace consisting of the closure in L2(∂D) of all holomorphic functions in D...