Analízis Tanszék

Előadó: Pap Margit (PTE)

Időpont: 2014.03.19.

In this talk I will present a multiresolution analysis in the Hardy space of the unit disc. The construction is an analogy with the discrete affine wavelet multiresolution, and in fact is the discretization of the continuous voice transform generated by a representation of the Blaschke group over the space H2(T). The levels of the multiresolution are generated by analytic wavelets i.e. by the Malmquist-Takenaka system, with a special localization of the poles. The n-th level of the multiresolution has finite dimension (in classical affine multiresolution this is not the case) and still we have the density property, i.e. the closure in norm of the reunion of the multiresolution levels is equal to the Hardy space. The projection operator to the n-th resolution level is in the same time a rational interpolation operator on a finite subset of quasi lattice points.
If we can measure the values of the function on the points of the quasi lattice the discrete wavelet coeffcients can be computed exactly. This makes our multiresolution approximation very useful from the view of the computational aspects. The theory of wavelet constructions on the Hardy space of the unit disc can be associated with time frequency-domain description of discrete-time-invariant dynamical systems. Using the Cayley transform an analogous construction in the Hardy space of the upper half plane can be made. The adapted description for the half-plane is used in system theory to describe the spectral behavior of continuous-time-invariant systems.