Analytic functionals and entire functionals on the complex light cone

Analytic Functionals and the Bergman Projection on Circular Domains

A property of the Bergman projection associated to a bounded circular domain containing the origin in C^ is proved: Functions which extend to be holomorphic in large neighborhoods of the origin are characterized as Bergman projections of smooth functions with small support near the origin. For certain circular domains D, it is also shown that functions which extend holomorphically to a neighbor...

Lorentz-covariant ultradistributions, hyperfunctions, and analytic functionals

We generalize the theory of Lorentz-covariant distributions to broader classes of functionals including ultradistributions, hyperfunctions, and analytic functionals with a tempered growth. We prove that Lorentz-covariant functionals with essential singularities can be decomposed into polynomial covariants and establish the possibility of the invariant decomposition of their carrier cones. We de...

Almost multiplicative linear functionals and approximate spectrum

We define a new type of spectrum, called δ-approximate spectrum, of an element a in a complex unital Banach algebra A and show that the δ-approximate spectrum σ_δ (a) of a is compact. The relation between the δ-approximate spectrum and the usual spectrum is investigated. Also an analogue of the classical Gleason-Kahane-Zelazko theorem is established: For each ε>0, there is δ>0 such that if ϕ is...

Analytic Bias Reduction for k-Sample Functionals

We give analytic methods for nonparametric bias reduction that remove the need for computationally intensive methods like the bootstrap and the jackknife. We call an estimate pth order if its bias has magnitude n 0 as n0 → ∞, where n0 is the sample size (or the minimum sample size if the estimate is a function of more than one sample). Most estimates are only first order and require O(N) calcul...

Analysis of Complex Brownian Functionals