Since we have the same product rule, quotient rule, sum rule, chain rule etc. available to us for differentiating complex functions, we already know many antiderivatives. For example, by differentiating f (z) = z one obtains f ′(z) = nzn−1, and from this one sees that the antiderivative of z is 1 n+1 z – except for the very important case where n = −1. Of course that special case is very import...

We adopt the following convention: x1, x2, z are sets, A is a non empty set, and f , g, h are elements of CA. Let us consider A. The functor +CA yielding a binary operation on CA is defined by: (Def. 1) For all elements f , g of CA holds +CA(f, g) = (+C)◦(f, g). Let us consider A. The functor ·CA yielding a binary operation on CA is defined as follows: (Def. 2) For all elements f , g of CA hold...

We survey a few classes of analytic functions on the disk that have real boundary values almost everywhere on the unit circle. We explore some of their properties, various decompositions, and some connections these functions make to operator theory.

We compute the disk potential of Gelfand–Zeitlin monotone torus fiber in a quadric hypersurface by exploiting toric degenerations, Lie theoretical mirror symmetry, and structural result Fukaya category.

In the present work, under some di¤erentiability conditions on the potential functions , we …rst reduce the inverse scattering problem (ISP) for the polynomial pencil of the Scroedinger equation to the corresponding ISP for the generalized matrix Scrödinger equation . Then ISP will be solved in analogy of the Marchenko method. We aim to establish an e¤ective algorithm for uniquely reconstructin...