Recently, we presented a new image pyramid, called the Riesz pyramid, that uses the Riesz transform to manipulate the phase in non-oriented sub-bands of an image sequence to produce real-time motion-magnified videos. In this report we give a quaternionic formulation of the Riesz pyramid, and show how several seemingly heuristic choices in how to use the Riesz transform for phase-based video mag...

We consider space-time continuous Galerkin methods with mesh modification in time for semilinear second order hyperbolic equations. We show a priori estimates in the energy norm without mesh conditions. Under reasonable assumptions on the choice of the spatial mesh in each time step we show optimal order convergence rates. Estimates of the jump in the Riesz projection in two successive time ste...

The one-dimensional chain of coupled oscillators with long-range power-law interaction is considered. The equation of motion in the infrared limit are mapped onto the continuum equation with the Riesz fractional derivative of order α, when 0 < α < 2. The evolution of soliton-like and breather-like structures are obtained numerically and compared for both types of simulations: using the chain of...

Let T=H+iK be hyponormal and Q be a strictly monotone increasing continuous function on s(H ). We define ~ Q(T ) by ~ Q(T )=Q(H )+iK. In this paper, we show that if z is an isolated eigenvalue of ~ Q(T ), then the corresponding Riesz projection is self-adjoint. Also we introduce Xia spectrum and study the existence of an invariant subspace of an operator ~ Q(T ).

We prove norm estimates for the difference of resolvents operators and their discrete counterparts, embedded into continuum using biorthogonal Riesz sequences. The are given in operator on square integrable functions, depend explicitly mesh size operators. a sum Fourier multiplier multiplicative potential. multipliers include fractional Laplacian pseudo-relativistic free Hamiltonian. potentials...

It is well known that any finite missing samples of a band-limited signal can be recovered from the remaining known samples when the signal is oversampled at a rate higher than the minimum Nyquist rate. We consider a similar problem for an oversampled signal in shift invariant spaces with compactly supported continuous Riesz generators. Using a multi-channel oversampling, we find conditions und...

There is an interesting potential theory associated to each degenerate elliptic, fully nonlinear equation f(Du) = 0. These include all the potential theories attached to calibrated geometries. This paper begins the study of tangents to the subsolutions in these theories, a topic inspired by the results of Kiselman in the classical plurisubharmonic case. Fundamental to this study is a new invari...