Hadamard transform

About: Hadamard transform is a research topic. Over the lifetime, 7262 publications have been published within this topic receiving 94328 citations.

The hadamard condition and kay's conjecture in (axiomatic) quantum field theory on curved space-time

Abstract: We interpret the global Hadamard condition for a two-point distribution of a Klein-Gordon neutral scalar quantum field model on an arbitrary globally hyperbolic curved space-time in terms of distinguished parametrices (of Duistermaat and Hörmander) and a wave front set spectrum condition. Microlocal results by Duistermaat and Hörmander such as the propagation of singularities theorem and the uniqueness of distinguished parametrices are employed in the proof. Using a smoothing, positivity-preserving pseudo-differential operator, one obtains a local-to-global singularity theorem, generalizing a conjecture by Kay that for quasi-free Klein-Gordon states, local Hadamard implies global Hadamard. This theorem relies on a general wave front set spectrum condition for the two-point distribution; a counterexample is given on Minkowski space when this condition is violated. We postulate a wave front set condition for any m-point distribution on a space-time and show consistency up to C with the usual spectrum condition on Minkowski space and exact correspondence with this condition in the scaling limit. Axioms implying a spin-statistics theorem are suggested for quantum field models on curved space-time.

System and method of operation for network overlay geolocation system with repeaters using am golay hadamard signatures

Abstract: A novel system and method for a network overlay geolocation system operating in a host wireless communication system with repeaters is disclosed. Embodiments of the novel system and method enable a wireless communication system to determine if signals being received by system receivers arrive directly from a target mobile appliance or if the signals are passing through or via a repeater. In an embodiment, the system's repeaters use a co-channel AM Golay Hadamard sequence multiplied by an uplink signal to watermark the repeated signal. The system uses the known AM Golay Hadamard sequences of the repeaters and the waveform of the received uplink signal to detect whether a repeater has operated on the signal and which repeater operated on the uplink signal. Embodiments of the novel system and method provide system management data and can be used to provide more accurate geolocation of mobiles served by repeater stations.

Hadamard States for the Vector Potential on Asymptotically Flat Spacetimes

Abstract: We develop a quantization scheme for the vector potential on globally hyperbolic spacetimes which realizes it as a locally covariant conformal quantum field theory. This result allows us to employ on a large class of backgrounds, which are asymptotically flat at null infinity, a bulk-to-boundary correspondence procedure in order to identify for the underlying field algebra a distinguished ground state which is of Hadamard form.

Fast polynomial transforms based on Toeplitz and Hankel matrices

Abstract: Many standard conversion matrices between coefficients in classical orthogonal polynomial expansions can be decomposed using diagonally-scaled Hadamard products involving Toeplitz and Hankel matrices. This allows us to derive $\smash{\mathcal{O}(N(\log N)^2)}$ algorithms, based on the fast Fourier transform, for converting coefficients of a degree $N$ polynomial in one polynomial basis to coefficients in another. Numerical results show that this approach is competitive with state-of-the-art techniques, requires no precomputational cost, can be implemented in a handful of lines of code, and is easily adapted to extended precision arithmetic.