相关论文: Elementary Proof of Moretti's Polar Decomposition …
In the setting of adjointable operators on Hilbert $C^*$-modules, this paper deals with the polar decomposition of the product of three operators. The relationship between the polar decompositions associated with three operators is…
Higher-rank versions of Wold decomposition are shown to hold for doubly commuting isometric representations of product systems of C*-correspondences over N^k, generalising the classical result for a doubly commuting pair of isometries due…
A nonlinear transformation in the momentum space is constructed which converts the deformed action of Lorentz and Weyl generators on momenta into the standard one.
The Lorentz transformations are represented by Einstein velocity addition on the ball of relativistically admissible velocities. This representation is by projective maps. The Lie algebra of this representation defines the relativistic…
Our goal here is to see the space of matrices of a given size from a geometric and topological perspective, with emphasis on the families of various ranks and how they fit together. We pay special attention to the nearest orthogonal…
The asymptotic performance of a polar code under successive cancellation decoding is determined by the exponent of its polarizing matrix. We first prove that the partial distances of a polarizing matrix constructed from the Kronecker…
A new method of derivation of Lorentz Transformation (LT) is given based on both axioms of special relativity (SR) and physical intuitions. The essence of the transformation is established and the crucial role played by the presumptions is…
We use standard constructions in algebraic geometry and homological algebra to extend the decomposition and hard Lefschetz theorems of T. Mochizuki and C. Sabbah so that they remains valid without the quasi-projectivity assumptions.
The Standard Model extension with additional Lorentz violating terms allows for redefining the equation of motion of a propagating left-handed fermionic particle. The obtained Dirac-type equation can be embedded in a generalized…
On compact Riemannian manifolds, we prove a decomposition theorem for arbitrarily bounded energy sequence of solutions of a singular elliptic equation.
We prove a local support theorem for the exponential Radon transform for functions of exponential decay at infinity. We also show that our decay condition is essentially sharp for the classical Radon transform for hyperbolic type domains as…
In this note we prove a representation theorem for the symmetric cone automorphisms in the spin algebra\, $\Ln$.
For each piecewise linear Lorenz map that expand on average, we show that it admits a dichotomy: it is either periodic renormalizable or prime. As a result, such a map is conjugate to a $\beta$-transformation.
The basic disentanglement theorem established by the present authors states that estimates on a weighted geometric mean over (convex) families of functions can be disentangled into quantitatively linked estimates on each family separately.…
This article introduces the Hartwig-Spindelb\"{o}ck decomposition of dual complex matrices. We provide representations of some generalized inverses using this decomposition. Further, several characterizations are established for a complex…
We systematically study the moduli theory of symplectic varieties (in the sense of Beauville) which admit a resolution by an irreducible symplectic manifold. In particular, we prove an analog of Verbitsky's global Torelli theorem for the…
The shortening of bodies in the direction of motion, Lorentz contraction, follows from the solution of Maxwell's equations. Moving light clocks will tick slower than those at rest because the speed of light does not depend on a source of…
We study generalized polar decompositions of densely defined, closed linear operators in Hilbert spaces and provide some applications to relatively (form) bounded and relatively (form) compact perturbations of self-adjoint, normal, and…
For theories with multiple couplings we construct simple expressions for the four-dimensional (or, in general, integer-dimensional) renormalization constants assuming that all divergences are logarithmical. These expressions allow relating…
Let $(X,D)$ be a smooth log pair over $\mathbb{C}$ such that the complement $U := X \setminus D$ carries a maximally varied family of polarized manifolds. We prove a version of second main theorem on $(X,D)$ by using the Viehweg-Zuo…