In this work we obtain positive bounded solutions of various perturbations \begin{document}$ \begin{equation} \left\{ \begin{array}{lcl} \hfill -\Delta u - \gamma \sum_{i, j = 1}^N \frac{x_i x_j}{|x|^2} u_{x_i x_j} & u^p \qquad \mbox{ in } B_1, \\ 0 \hfill\qquad\ on \partial \end{array}\right. \end{equation} \ (1) $\end{document} where $ B_1 is the unit ball {{\mathbb{R}}}^N N \ge 3 $, \gam...

In this paper, we discuss the following conjecture raised by BaumDouglas: For any first-order elliptic differential operator D on smooth manifold M with boundary dM , D possesses an elliptic boundary condition if and only if d[D] = 0 in Kx(dM), where [D] is the relative AT-cycle in K0(M, dM) corresponding to D . We prove the "if part of this conjecture for dim(M) ± 4, 5, 6, 7 and the "only if p...

Using Krattenthaler’s operator method, we give a new proof of Warnaar’s recent elliptic extension of Krattenthaler’s matrix inversion. Further, using a theta function identity closely related to Warnaar’s inversion, we derive summation and transformation formulas for elliptic hypergeometric series of Karlsson–Minton-type. A special case yields a particular summation that was used by Warnaar to ...

We study the adjointness problem for the closed extensions of a general b-elliptic operator A ∈ x Diffmb (M ;E), ν > 0, initially defined as an unbounded operator A : C∞ c (M ;E) ⊂ x L b (M ;E) → xL b (M ;E), μ ∈ R. The case where A is a symmetric semibounded operator is of particular interest, and we give a complete description of the domain of the Friedrichs extension of such an operator.

In this paper we build on the framework developed in [7, 8, 9] to obtain a more complete understanding of the gluing properties for indices of boundary value problems for the SpinC-Dirac operator with sub-elliptic boundary conditions. We extend our analytic results for sub-elliptic boundary value problems for the SpinC-Dirac operator, and gluing results for the indices of these boundary problem...