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...

In this paper, we introduce the notion of biorthogonal wavelet packets associated with nonuniform multiresoltion analysis and study their characteristics by means of Fourier transform. Three biorthogonal formulas regarding these wavelet packets are established. Moreover, it is shown how to obtain several new Riesz bases of the space (R) by constructing a series of subspaces of these nonuniform ...

The Choquet integral is defined for a real function with respect to a fuzzy measure taking values in a complete Riesz space. As applications there are presented: constructions of belief and plausibility measures, the formulation of an extension principle, and the Möbius transform for vector values measures.

We prove a weighted norm inequality for the maximal Bochner-Riesz operator and the associated square-function. This yields new L(R) bounds on classes of radial Fourier multipliers for p ≥ 2 + 4/d with d ≥ 2, as well as space-time regularity results for the wave and Schrödinger equations.

In this dissertation, we study the Feichtinger Conjecture(FC), which has been shown to be equivalent to the celebrated Kadison-Singer Problem. The FC states that every norm-bounded below Bessel sequence in a Hilbert space can be partitioned into finitely many Riesz basic sequences. This study is divided into two parts. In the first part, we explore the FC in the setting of reproducing kernel Hi...

We employ an operator theoretic setting established in [2]. Under Condition 2.1 below, a self-adjoint (actually quasi-uniformly positive [7]) operator A in the Krein space L2,r(−1, 1)⊕C 2 ∆ is associated with the eigenvalue problem (1.1), (1.2). Here ∆ is a 2 × 2 nonsingular Hermitean matrix which is determined by M and N; see Section 2 for details. We remark that the topology of this Krein spa...

We show that there exists a bounded subset of $\mathbb{R}$ such no system exponentials can be Riesz basis for the corresponding Hilbert space. An additional result gives lower bound constant any putative two dimensional disk.

Abstract. A Banach space X is called an HT space if the Hilbert transform is bounded from L(X) into L(X), where 1 < p < ∞. We introduce the notion of an ACF Banach space, that is, a Banach space X for which we have an abstract M. Riesz Theorem for conjugate functions in L(X), 1 < p < ∞. Berkson, Gillespie, and Muhly [5] showed that X ∈ HT =⇒ X ∈ ACF. In this note, we will show that X ∈ ACF =⇒ X...

In this paper, we give a new definition of the flux of a superharmonic function defined outside a compact set in a Brelot space without positive potentials. We also give a new notion of potential in a BS space (that is, a harmonic space without positive potentials containing the constants) which leads to a Riesz decomposition theorem for the class of superharmonic functions that have a harmonic...

In this paper, we give a characterization of compact sets in Lp-spaces on metric measure spaces, which is generalization the Kolmogorov-Riesz theorem. Using criterion, investigate topological type space consisting Lipschitz maps with bounded supports.