This extended write–up of my talk gives an introductory survey of mathematical problems of the quantization of gauge systems. Using the Schwinger model as an exactly tractable but nontrivial example which exhibits general features of gauge quantum field theory, I cover the following subjects: The axiomatics of quantum field theory, formulation of quantum field theory in terms of Wightman functi...

We introduce the notion of quasi-inner function and show that product u = ρ ∞ ∏ v m + 1 ratios local L -factors ( z ) γ / − over a finite set F places Q inclusive archimedean place is on left critical line ℜ 2 in following sense. The off diagonal part 21 matrix multiplication by orthogonal decomposition Hilbert space square integrable functions into Hardy H its complement compact operator. When...

Let H. (resp., H ) be a real and separable Hubert space with Borel O'field T (resp., rj, and let (H. X //-, T, X T.) be the product measurable space generated by the measurable rectangles. This paper develops relations between probability measures on (H. x H , V x T.), i.e., joint measures, and the projections of such measures on (H., T.) and (H , Y ). In particular, the class of all joint Gaus...

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...

This paper considers the construction of Reproducing Kernel Hilbert Spaces (RKHS) on the sphere as an alternative to the conventional Hilbert space using the inner product that yields the L(S) function space of finite energy signals. In comparison with wavelet representations, which have multi-resolution properties on L(S), the representations that arise from the RKHS approach, which uses diffe...