Given a complex manifold M endowed with a hermitian metric g and supporting a smooth probability measure μ, there is a naturally associated Dirichlet form operator A on L(μ). If b is a function in L(μ) there is a naturally associated Hankel operator Hb defined in holomorphic function spaces over M . We establish a relation between hypercontractivity properties of the semigroup e−tA and boundedn...

We derive a spectral method for unsupervised learning of Weighted Context Free Grammars. We frame WCFG induction as finding a Hankel matrix that has low rank and is linearly constrained to represent a function computed by inside-outside recursions. The proposed algorithm picks the grammar that agrees with a sample and is the simplest with respect to the nuclear norm of the Hankel matrix.

where φ :Rn → C and φt(x)= t−nφ(x/t), t > 0. For conditions of validity of identity (1.1), we may refer to [3]. Hankel convolution introduced by Hirschman Jr. [5] related to the Hankel transform was studied at length by Cholewinski [1] and Haimo [4]. Its distributional theory was developed byMarrero and Betancor [6]. Pathak and Pandey [8] used Hankel convolution in their study of pseudodifferen...

Nuclearity of the Hankel operator is a known sufficient condition for convergence of Lyapunov-balanced truncations. We show how a previous result on nuclearity of Hankel operators of systems with an analytic semigroup can be extended to systems with a semigroup of class D with p ≥ 1 (the case p = 1 being the analytic case). For semigroups that are generated by a Dunford-Schwartz spectral operat...

We describe a new method to compute general cubature formulae. The problem is initially transformed into the computation of truncated Hankel operators with flat extensions. We then analyze the algebraic properties associated to flat extensions and show how to recover the cubature points and weights from the truncated Hankel operator. We next present an algorithm to test the flat extension prope...

We study a constructive method of rational approximation of analytic functions based on ideas of the theory of Hankel operators. Some properties of the corresponding Hankel operator are investigated. We also consider questions related to the convergence of rational approximants. Analogues of Montessus de Ballore’s and Gonchars’s theorems on the convergence of rows of Padé approximants are proved.

Let La be a Bergman space. We are interested in an intermediate Hankel operator H M φ from La to a closed subspace M of L 2 which is invariant under the multiplication by the coordinate function z. It is well known that there do not exist any nonzero finite rank big Hankel operators, but we are studying same types in case H φ is close to big Hankel operator. As a result, we give a necessary and...

This paper studies lower bounds for arithmetic circuits computing (non-commutative) polynomials. Our conceptual contribution is an exact correspondence between circuits and weighted automata: algebraic branching programs are captured by weighted automata over words, and circuits with unique parse trees by weighted automata over trees. The key notion for understanding the minimisation question o...

Weighted averaging is said to be optimal when the weights assigned to the cues minimize the variance of the final estimate. Since the variance of this optimal percept only depends on the variances of the individual cues, irrespective of their values, judgments about a cue conflict stimulus should have the same variance as ones about a cue consistent stimulus. We tested this counter-intuitive pr...