Trotter-Kato product formula for unitary groups

Let $A$ and $B$ be non-negative self-adjoint operators in a separable Hilbert space such that its form sum $C$ is densely defined. It is shown that the Trotter product formula holds for imaginary times in the $L^2$-norm, that is, one has % % \begin{displaymath} \lim_{n\to+\infty}\int^T_0 \|(e^{-itA/n}e^{-itB/n})^nh - e^{-itC}h\|^2dt = 0 \end{displaymath} % % for any element $h$ of the Hilbert space and any $T > 0$. The result remains true for the Trotter-Kato product formula % % \begin{displaymath} \lim_{n\to+\infty}\int^T_0 \|(f(itA/n)g(itB/n))^nh - e^{-itC}h\|^2dt = 0 \end{displaymath} % % where $f(\cdot)$ and $g(\cdot)$ are so-called holomorphic Kato functions; we also derive a canonical representation for any function of this class

On the basicity of unitary system of exponents in the variable exponent Lebesgue spaces

In the present work it is considered the system of functions a (t) e int −b (t) e −int , n ∈ N, with complex-valued coefficients a (·) ; b (·) : [0, π] → C. Sufficient conditions on the coefficients of the system are found in order for the system to form a basis in Lebesgue spaces with variable exponent

An Induction Principle for the Weighted p-Energy Minimality of x/|x|

In this paper, we investigate minimizing properties of the map $x/\|x\|$ from the Euclidean unit ball $\mathbf{B}^{n}$ to its boundary $\mathbb{S}^{n-1}$, for the weighted energy functionals $E^n\_{p,\alpha}(u)=\int\_{\mathbf{B}^{n}} \|x\|^{\alpha}\|\nabla u\|^p dx$. We establish the following induction principle: if the map $\frac{x}{\|x\|}:\mathbf{B}^{n+1}\to \mathbb{S}^n$ minimizes $E^{n+1}\_{p,\alpha}$ among the maps $u: \mathbf{B}^{n+1}\to \mathbb{S}^n$ satisfying $u(x)=x$ on $\mathbb{S}^n$, then the map $\frac{y}{\|y\|}:\mathbf{B}^n\to\mathbb{S}^{n-1}$ minimizes $E^{n}\_{p,\alpha+1}$ among the maps $v: \mathbf{B}^n\to\mathbb{S}^{n-1}$ satisfying $v(y)=y$ on $\mathbb{S}^{n-1}$. This result enables us to enlarge the range of values of $p$ and $\alpha$ for which $x/\|x\|$ minimizes $E^n\_{p,\alpha}$.Comment: 8 page

D_{s0}^+(2317) as an iso-triplet four-quark meson

Although assigning D_{s0}^+(2317) to the I_3=0 component of iso-triplet four-quark mesons is favored by experiments, its neutral and doubly charged partners have not yet been observed. It is discussed why they were not observed in inclusive e^+e^- annihilation experiments and that they can be observed in B decays.Comment: 3 pages, 5 figures, invited talk at QNP06, the 4th Int. Conf. on Quarks and Nuclear Physics, June 5 - 10, 2006, Madri

CP Violation in Top Physics at the NLC

Top quark is extremely sensitive to non-standard CP violating phases. General strategies for exposing different types of phases at the NLC are outlined. SUSY phase(s) cause PRA in $t\to Wb$. The transverse polarization of the $\tau$ in the reaction $t\to b\tau\nu$ is extremely sensitive to a phase from the charged Higgs sector. Phase(s) from the neutral Higgs sector cause appreciable dipole moment effects and lead to sizable asymmetries in $e^+e^-\to t\bar tH^0$ and $e^+e^-\to t\bar t\nu_e\bar\nu_e$.}]Comment: 4 pages, Latex, 2 figures. For the Proceedings of the 28th Int. Conf. on HEP, Warsaw(July 1996