We describe a model for capturing the statistical structure of local amplitude and local spatial phase in natural images. The model is based on a recently developed, factorized third-order Boltzmann machine that was shown to be effective at capturing higher-order structure in images by modeling dependencies among squared filter outputs [1]. Here, we extend this model to Lp-spherically symmetric...

For an exotic locally compact Hausdorff space $L$, constructed under the assumption of Ostaszewski's $\clubsuit$-principle, and a countable ordinal $\alpha$, we prove that all operators defined on $C_0(\alpha\times L)$ are as simple possible. We also investigate geometry such classify up to isomorphisms its complemented subspaces.

Mφ : H → H for φ ∈ H∞(Ω). We mention some known results in this area that serve as a motivation for the present paper. First, if H is the classical Hardy space of the unit disk D, and if φ is an inner function on D, then Mφ is a pure isometry and a shift operator on H , and so its reducing subspaces are in a one-to-one correspondence with the closed subspaces of H (φH). Therefore, the reducing ...

We construct symmetric convex bodies that are not intersection bodies, but all of their central hyperplane sections are intersection bodies. This result extends the studies by Weil in the case of zonoids and by Neyman in the case of subspaces of Lp.

We prove that for any separable Banach space X, there exists a compact metric space which is homeomorphic to the Cantor space and whose Lipschitz-free space contains a complemented subspace isomorphic to X. As a consequence we give an example of a compact metric space which is homeomorphic to the Cantor space and whose Lipschitz-free space fails the approximation property and we prove that ther...

A Banach space is polyhedral if the unit ball of each of its finite dimensional subspaces is a polyhedron. It is known that a polyhedral Banach space has a separable dual and is c0-saturated, i.e., each closed infinite dimensional subspace contains an isomorph of c0. In this paper, we show that the Orlicz sequence space hM is isomorphic to a polyhedral Banach space if limt→0 M(Kt)/M(t) = ∞ for ...

is the dual group of G, and p ′ the conjugate exponent of p. An operator T between Banach spaces X and Y is said to be compatible with the Fourier transform F G if F G ⊗ T : Lp(G)⊗X → Lp′ (G ′ )⊗ Y admits a continuous extension [F , T ] : [Lp(G), X ] → [Lp′ (G ′ ), Y ]. We show that if G is topologically isomorphic with R×Z×F, where l and m are nonnegative integers and F is a compact group with...

In 1953 A. Grothendieck introduced the property known as Dunford-Pettis property [18]. A Banach space X has the Dunford-Pettis property (DPP in the sequel) if whenever (xn) and (ρn) are weakly null sequences in X and X∗, respectively, we have ρn(xn) → 0. It is due to Grothendieck that every C(K )-space satisfies the DPP. Historically, were Dunford and Pettis who first proved that L1(μ) satisfie...

Given an embedding of a smooth projective curve X genus g ? 1 into P N , we study the locus linear subspaces codimension 2 such that projection from said subspace, composed with embedding, gives Galois morphism ? . For prove this is variety components isomorphic to spaces. If = and given by complete system, also whose positive-dimensional are bundles over étale quotients elliptic curve, describ...