The spectrum εn has a Brillouin-zone like structure with Ω the width of the first zone, i.e. for any solution |un(t)〉 of quasienergy εn, and any integer m, exp(imΩt)|un(t)〉 is also a solution, with eigenvalue εn + mΩ. The states |un(t)〉 form a Hilbert space of T-periodic functions. The inner product in this space can be defined starting from the standard bra-ket inner product 〈•|•〉 for time-ind...

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...

this paper is an investigation of $l$-dual frames with respect to a function-valued inner product, the so called $l$-bracket product on $l^{2}(g)$, where g is a locally compact abelian group with a uniform lattice $l$. we show that several well known theorems for dual frames and dual riesz bases in a hilbert space remain valid for $l$-dual frames and $l$-dual riesz bases in $l^{2}(g)$.

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...

We investigate some properties of approximately quasi inner generalized dynamics and quasi approximately inner generalized derivations on modules. In particular, we prove that if A is a C*-algebra, is the generator of a generalized dynamics on an A-bimodule M satisfying and there exist two sequences of self adjoint elements in A such that for all in a core for , , then is approx...

We formulate a variational principle for a collection of projectors in an indefinite inner product space. The existence of minimizers is proved in various situations. In a recent book it was proposed to formulate physics with a new variational principle in space-time [2]. In the present paper we construct minimizers of this variational principle. In order to make the presentation self-contained...