We study divisibilities between bounded holomorphic quasi-inner functions in H∞ and operator-valued bounded holomorphic quasi-inner functions in H∞(Ω, L(K)) where Ω is a bounded finitely connected region. Furthermore, we characterize these divisibilities by using rationally-invariant subspaces.

We wish to describe how the hyperbolic geometry of a Riemann surface of genus g y g > 2, leads to a symplectic geometry on Tg, the genus g Teichmüller space, and ~Mg, the moduli space of genus g stable curves. The symplectic structure has three elements: the Weil-Petersson Kahler form, the FenchelNielsen vector fields t+, and the geodesic length functions I*. Weil introduced a Kahler metric for...

A mapping f : M → N between Hilbert C∗-modules approximately preserves the inner product if ‖〈f(x), f(y)〉 − 〈x, y〉‖ ≤ φ(x, y), for an appropriate control function φ(x, y) and all x, y ∈ M. In this paper, we extend some results concerning the stability of the orthogonality equation to the framework of Hilbert C∗modules on more general restricted domains. In particular, we investigate some asympt...

For a family of compact Riemann surfaces Xt of genus g > 1, parameterized by the Schottky space Sg, we define a natural basis of H(Xt, ω n Xt ) which varies holomorphically with t and generalizes the basis of normalized abelian differentials of the first kind for n = 1. We introduce a holomorphic function F (n) on Sg which generalizes the classical product ∏ ∞ m=1 (1 − q) for n = 1 and g = 1. W...

Masking is a popular countermeasure against side channel attacks. Many practical works use Boolean masking because of its simplicity, ease of implementation and comparably low performance overhead. Some recent works have explored masking schemes with higher algebraic complexity and have shown that they provide more security than Boolean masking at the cost of higher overheads. In particular, ma...

Masking schemes are a prominent countermeasure to defeat power analysis attacks. One of their core ingredients is the encoding function. Due to its simplicity and comparably low complexity overheads, many masking schemes are based on a Boolean encoding. Yet, several recent works have proposed masking schemes that are based on alternative encoding functions. One such example is the inner product...

In [59], we introduced an invariant of K3 surfaces with involution, which we obtained using equivariant analytic torsion. This invariant gives rise to a function on the moduli space of K3 surfaces with involution and is expressed as the Petersson norm of an automorphic form characterizing the discriminant locus. In this paper, we study the structure of this automorphic form. Under certain assum...

Suppose that A is a C^*-algebra. We consider the class of A-linear mappins between two inner product A-modules such that for each two orthogonal vectors in the domain space their values are orthogonal in the target space. In this paper, we intend to determine A-linear mappings that preserve orthogonality. For this purpose, suppose that E and F are two inner product A-modules and A+ is the set o...

We use ending laminations for Weil-Petersson geodesics to establish that bounded geometry is equivalent to bounded combinatorics for WeilPetersson geodesic segments, rays, and lines. Further, a more general notion of non-annular bounded combinatorics, which allows arbitrarily large Dehn-twisting, corresponds to an equivalent condition for Weil-Petersson geodesics. As an application, we show the...