Quasiconformal Whitney Partition
Whitney partition is a very important concept in modern analysis. We discuss here a quasiconformal version of the Whitney partition that can be usefull for Sobolev spaces.
math.FA↗
arXiv subjects
Nahum Zobin
Publications and source records attributed to Nahum Zobin.
On planar Sobolev $L^m_p$-extension domains
For each $m\ge 1$ and $p>2$ we characterize bounded simply connected Sobolev $L^m_p$-extension domains $Ω\subset R^2$. Our criterion is expressed in terms of certain intrinsic subhyperbolic metrics in $Ω$. Its proof is based on a series of results related to the existence of special chains of squares joining given points $x$ and $y$ in $Ω$. An important geometrical ingredient for obtaining these results is a new "Square Separation Theorem". It states that under certain natural assumptions on the relative positions of a point $x$ and a square $S\subsetΩ$ there exists a similar square $Q\subsetΩ$ which touches $S$ and has the property that $x$ and $S$ belong to distinct connected components of $Ω\setminus Q$.
math.FA↗
Failure of the Weierstrass Preparation Theorem in quasi-analytic Denjoy-Carleman rings
It is shown that Denjoy-Carleman quasi-analytic rings of germs of functions in two or more variables fail to satisfy the Weierstrass Preparation Theorem. The result is proven via a non-extension theorem.
math.CA↗
Fubctional integral approach to quantum gauge theories on a noncommutative space-time
We propose a construction of actions of a quantum gauge field theory on a noncommutative space-time, based on a Fourier transform on the Doplicher-Fredenhagen-Roberts group. This approach leads to a functional integral representation of the action, which in turn leads to considering the space of probability measures on the classical space-time as a noncommutative version of the space-time. This approach allows a very natural treatment of gauge fields terms in the action.
quant-ph↗
Noncommutative Gauge Theory without Lorentz Violation
The most popular noncommutative field theories are characterized by a matrix parameter theta^(mu,nu) that violates Lorentz invariance. We consider the simplest algebra in which the theta-parameter is promoted to an operator and Lorentz invariance is preserved. This algebra arises through the contraction of a larger one for which explicit representations are already known. We formulate a star product and construct the gauge-invariant Lagrangian for Lorentz-conserving noncommutative QED. Three-photon vertices are absent in the theory, while a four-photon coupling exists and leads to a distinctive phenomenology.
hep-th↗