We study the wavelet transform of functions invariant under a symmetry group, where the wavelet transform is associated to an irreducible unitary group representation. Among other results a new inversion formula and a new covariance principle are derived. As main examples we discuss the continuous wavelet transform and the short time Fourier transform of radially symmetric functions on R. 2000 ...

In a previous paper, we introduced a new interpretation of matrix models, in which any d-dimensional curved space can be realized in terms of d matrices, and the diffeomorphism and the local Lorentz symmetries are included in the ordinary unitary symmetry of the matrix model. Furthermore, we showed that the Einstein equation is naturally obtained, if we employ the standard form of the action, S...

We estimate the coupling of the K∗ vector meson to the N → Θ transition employing unitary symmetry, vector meson dominance, and results from the GRAAL Collaboration for η photoproduction off the neutron. Our small numerical value for the coupling constant is consistent with the nonobservation of the Θ in recent CLAS searches for its photoproduction. We also estimate the K∗coupling for the N → Σ...

A novel unitary directional wavelet methodology producing six complex-valued subbands per level of decomposition has been previously introduced [1,2] as a method of spatio-frequency decomposition for image fusion applications. Properties of the decomposition include unitarity, sparse computation, energy-packing efficiency, symmetry, and sub-pixel registration of all subbands at the same scale. ...

We study the compatibility between conformal symmetry together with unitarity and continuous higher-form symmetries. show that d-dimensional unitary field theories are not consistent p-form symmetries for certain (d,p), assuming corresponding conserved current is a primary operator. further discuss several dynamical applications of this constraint.

We consider a charged quantum particle in a random magnetic field with Gaussian, delta-correlated statistics. We show that although the single particle properties are peculiar, two particle quantities such as the diffusion constant can be calculated in perturbation theory. We map the problem onto a non-linear sigma-model for Q-matrices of unitary symmetry with renormal-ized diffusion coefficien...

We give a constructive proof for the superbosonization formula for invariant random matrix ensembles, which is the supersymmetry analog of the theory of Wishart matrices. Formulas are given for unitary, orthogonal and symplectic symmetry, but worked out explicitly only for the orthogonal case. The method promises to become a powerful tool for investigating the universality of spectral correlati...

We give a constructive proof for the superbosonization formula for invariant random matrix ensembles, which is the supersymmetry analog of the theory of Wishart matrices. Formulas are given for unitary, orthogonal and symplectic symmetry, but worked out explicitly only for the orthogonal case. The method promises to become a powerful tool for investigating the universality of spectral correlati...

In this paper we show how the symmetry present in many linear systems can be exploited to significantly reduce the computational effort required for controller synthesis. This approach may be applied when controller design specifications are expressible via semidefinite programming. In particular, when the overall system description is invariant under unitary coordinate transformations of the s...

We describe the inequalities on the possible eigenvalues of products of unitary matrices in terms of quantum Schubert calculus. Related problems are the existence of flat connections on the punctured two-sphere with prescribed holonomies, and the decomposition of fusion product of representations of SU(n), in the large level limit. In the second part of the paper we investigate how various aspe...