Hankel Operators and Their Applications

By V. Peller. IEEE Transactions on Automatic Control, 2003

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In Applied Mathematics

Citations in the corpus

Szegö's theorem and its probabilistic descendants (2011, background): “ForH, one has a version of the FeffermanStein decomposition for BMO: f ∈ H ⇔ f = u+ ṽ, u, v ∈ H ∩ L ([Pel] §7.”
Multiple operator integrals and higher operator derivatives (2005, background): “from the nuclearity criterion for Hankel operators (see the monograph [Pe4]) and it implies that the condition φ ∈ C1(R) is not sufficient.”
An explicit formula for the cubic Szegö equation (2013, neutral): “Notice that this deﬁnition is diﬀerent from the standard ones used in references [9], [11], where Hankel operators are rather deﬁned as linear operators from L 2 + into its orthogonal complement.”
Integral operators mapping into the space of bounded analytic functions (2016, background): “Theorem 2.4 below allows us to describe those g ∈ H(D) such that Tg : X → H∞ is bounded when X is an Lp-quotient, in particular, when X is the Bloch space or BMOA.”
On approximation of functions by exponential sums (2005, methodology): “In this sense our approach can be understood as a nite dimensional version of the theory of Adamjan, Arov, and Kre n (AAK theory), which involves innite Hankel matrices as a tool for constructing rational approximations [1,2,3] (for a recent exposition see [ 25 ]).”
Functions of normal operators under perturbations (2010, methodology): “Note also that the necessary conditions obtained in [Pe1] and [Pe2] are based on the trace class criterion for Hankel operators, see [Pe1] and [Pe4], Ch.”
Invariant tori for the cubic Szegö equation (2010, methodology): “We introduce the compressed shift operator ([11], [12], [13]) S := PuTz , where Pu denotes the orthogonal projector onto the closure of the range of Hu.”
A Hankel matrix acting on Hardy and Bergman spaces (2010, background): “In many papers (see [CS], [JPS], [T], [PV] and [Pe]), another approach to the study of Hankel operators on spaces of analytic functions is developed, using the symbol of the operator, which in our case is essentially the function (1.”
Scattering Systems with Several Evolutions and Multidimensional Input/State/Output Systems (2005, background): “Remark 6.6. Theorem 6.5 plays in our setting a role analogous to one direction of the classical Kronecker Theorem on Hankel operators of finite rank (see, e.g., [ 33, Section 1.3 ]).”
An extension of the Koplienko-Neidhardt trace formulae (2004, background): “In [Pe1] and [Pe2] with the help of the nuclearity criterion for Hankel operators (see recent monograph [Pe4]) necessary conditions (in terms of Besov classes and Carleson measures) were found on φ for the operator φ(B) − φ(A) (or φ(V ) − φ(U)) to belong to S1.”
Norm of the Hilbert matrix on Bergman and Hardy spaces and a theorem of Nehari type (2008, background): “Several interesting facts about the Hilbert matrix are described in [1] and [7, Problems 46-48] and further results about the spectrum of H can be found in [15].”
Multiple operator integrals in perturbation theory (2015, methodology): “By the trace class criterion for Hankel operators [Pe1] (see also [Pe6], Ch.”