Time-dependent angularly averaged inverse transport

This paper concerns the reconstruction of the absorption and scattering parameters in a time-dependent linear transport equation from knowledge of angularly averaged measurements performed at the boundary of a domain of interest. We show that the absorption coefficient and the spatial component of the scattering coefficient are uniquely determined by such measurements. We obtain stability results on the reconstruction of the absorption and scattering parameters with respect to the measured albedo operator. The stability results are obtained by a precise decomposition of the measurements into components with different singular behavior in the time domain

On Bochner-Krall orthogonal polynomial systems

In this paper we address the classical question going back to S. Bochner and H. L. Krall to describe all systems $\{p_{n}(x)\}_{n=0}^\infty$ of orthogonal polynomials (OPS) which are the eigenfunctions of some finite order differential operator. Such systems of orthogonal polynomials are called Bochner-Krall OPS (or BKS for short) and their spectral differential operators are accordingly called Bochner-Krall operators (or BK-operators for short). We show that the leading coefficient of a Nevai type BK-operator is of the form $((x - a)(x-b))^{N/2}$. This settles the special case of the general conjecture 7.3. of [4] describing the leading terms of all BK-operators

On Bochner-Krall orthogonal polynomial systems

In this paper we address the classical question going back to S. Bochner and H. L. Krall to describe all systems $\{p_{n}(x)\}_{n=0}^\infty$ of orthogonal polynomials (OPS) which are the eigenfunctions of some finite order differential operator. Such systems of orthogonal polynomials are called Bochner-Krall OPS (or BKS for short) and their spectral differential operators are accordingly called Bochner-Krall operators (or BK-operators for short). We show that the leading coefficient of a Nevai type BK-operator is of the form $((x - a)(x-b))^{N/2}$. This settles the special case of the general conjecture 7.3. of [4] describing the leading terms of all BK-operators

PLATO - Plattform Orbiter. Ein zukuenftiger Mehrzweckwiedereintrittskoerper. Durchfuehrbarkeitsstudie. Technische Berichte. Bd. 2

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