The exterior Calderón operator for non-spherical objects

The Harmonic Operator for Exterior Differential Forms.

Image-based BRDF Acquisition for Non-spherical Objects

In order to create photorealistic images, we need to know how light is reflected from different materials. The bidirectional reflectance distribution functions (BRDF) plays an important role in modeling the reflectance of materials. This paper presents a framework for extracting BRDF samples from multiple photographs, which are taken from the same viewpoint but under different lighting directio...

The Spherical Tensor Gradient Operator

The spherical tensor gradient operator Y l (∇), which is obtained by replacing the Cartesian components of r by the Cartesian components of ∇ in the regular solid harmonic Y l (r), is an irreducible spherical tensor of rank l. Accordingly, its application to a scalar function produces an irreducible spherical tensor of rank l. Thus, it is in principle sufficient to consider only multicenter int...

Strong Converse Inequality for a Spherical Operator

In the paper titled as “Jackson-type inequality on the sphere” 2004 , Ditzian introduced a spherical nonconvolution operator Ot,r , which played an important role in the proof of the wellknown Jackson inequality for spherical harmonics. In this paper, we give the lower bound of approximation by this operator. Namely, we prove that there are constants C1 and C2 such that C1ω2r f, t p ≤ ‖Ot,rf − ...

Injectivity of the spherical means operator

Let S be a surface in R which divides the space into two connected components D1 and D2. Let f ∈ C0(R) be some real-valued compactly supported function with supp f ⊂ D1. Consider Mf := m(y, r) := ∫ Rn f(z)δ(|y − z| − r)dz, where δ is the delta-function, y ∈ S and r > 0 are arbitrary. A general, local at infinity, condition on S is given, under which M is injective, that is, Mf = 0 implies f = 0...