## Ana Paula Nolasco

## Wedge Diffraction Problems with Rational Angles for Dirichlet and Neumann Boundary Conditions

The explicit representation of waves diffracted from non-rectangular wedges belongs to a famous class of open problems in diffraction theory. These problems are often modelled by Dirichlet or Neumann boundary value problems for the 2D Helmholtz equation with complex wave number. Using analytical methods for boundary integral operators (more precisely, pseudodifferential operators) together with symmetry arguments, we solve explicitly a number of reference problems for the Helmholtz equation regarding rational wedge angles (α = πm/n, m,n em IN), Dirichlet and Neumann boundary conditions, in a Sobolev spaces framework.

The talk is based on a joint work with F.-O. Speck and T. Ehrhardt.

The talk is based on a joint work with F.-O. Speck and T. Ehrhardt.

Manuela Rodrigues

## Fractional circle Zernike polynomials

We present a fractional extension of the classical disc Zernike polynomials deﬁned via g-Jacobi functions. Some properties of this new class of functions are studied, such as discrete and continuous orthogonality relations, recurrence relations for consecutive and distant neighborhoods, and diﬀerential relations. A graphic representation for the proposed fractional circle Zernike polynomials will be presented, as well as, its comparison with the classical case.

Joint work with N. Vieira.

Joint work with N. Vieira.