Resolvent Estimates in (weighted) Lp spaces for the Stokes Operator in Lipschitz Domains

Recently, by Z. Shen, resolvent estimates for the Stokes operator were established in <i>L^p(Ω) </i>when <i>Ω</i> is a Lipschitz domain in <i>R^d</i>, with <i>d≥3</i> and<i> |1/p-1/2|&lt;1/(2d)+ε</i>. This result implies that the Stokes operator generates a bounded analytic semigroup in <i>L^p(Ω)</i> in the case...

Generation of wavelets by semigroups

Wavelets are a recent development in signal processing. These kind of functions<br/>are both well-localized in time and in frequency, and so using these to transform the signal gives insight where certain frequencies are needed. The classical way of constructing wavelets, as described by Daubechies and Meyer [3,9] is only well-suited for the...

Boundary values of analytic functions on the disc

In this bachelor's thesis we will solve the Dirichlet problem with an L^p(T) boundary function. First, we will focus on the holomorphic version of the Dirichlet problem and introduce Hardy space theory, from which will follow a sufficient condition on the Fourier coefficients of the boundary function. Then we will prove the...