Analytic Extension by Hausdorff Methods

Hausdorff-analytic Functions of Matrices1

Analytic Hausdorff Gaps Ii: the Density Zero Ideal

We prove two results about the quotient over the asymptotic density zero ideal. First, it is forcing equivalent to P(N)/Fin ∗Rc, where Rc is the homogeneous probability measure algebra of character c. Second, if it has analytic Hausdorff gaps then they look considerably different from previously known gaps of this form. We consider density ideals, ideals of the form Zμ = {A| lim supn μn(A) = 0}...

Local monotonicity of Hausdorff measures restricted to real analytic curves

We prove that the 1-dimensional Hausdorff measure restricted to a simple real analytic curve γ : R → R , N ≥ 2, is locally 1-monotone.

Analytic solutions of fractional differential equations by operational methods

We describe a general operational method that can be used in the analysis of fractional initial and boundary value problems with additional analytic conditions. As an example, we derive analytic solutions of some fractional generalisation of differential equations of mathematical physics. Fractionality is obtained by substituting the ordinary integer-order derivative with the Caputo fractional ...

Analytic Methods for Select Sets

We analyze the asymptotic number of items chosen in a selection procedure. The procedure selects items whose rank among all previous applicants is within the best 100p percent of the number of previously selected items. We use analytic methods to obtain a succinct formula for the first-order asymptotic growth of the expected number of items chosen by the procedure.