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On super weakly compact convex sets and representation of {m swcc}(X)^*
super weakly compact set dual of normed semigroup uniform Fr'echet differetiability representation
2011/10/20
In this note, we give first that a characterization of super weakly compact convex sets of a Banach space X, namely, a sufficient and necessary condition for a closed bounded convex set Ksubset X to b...
Exceptional sets of projections, unions of k-planes, and associated transforms
dimension projection k-plane Fourier transform
2011/9/20
Abstract: We prove a generalization of a result of Peres and Schlag on the dimensions of certain exceptional sets of projections and then apply it to a geometric problem.
Bounds For Multilinear Sublevel Sets Via Szemeredi's Theorem
Multilinear Sublevel Sets Szemeredi's Theorem Classical Analysis and ODEs
2011/9/5
Abstract: In 2005, Li, Tao, Thiele and the author raised a general question concerning upper bounds for a class of multilinear oscillatory integral operators, and established such bounds in a few case...
The finite cardinalities of level sets of the Takagi function
Takagi function Nowhere-differentiable function Level set Self-similarity Takagi expansion
2011/8/25
Abstract: Let T be Takagi's continuous but nowhere-differentiable function. It is known that almost all level sets (with respect to Lebesgue measure on the range of T) are finite. We show that the mos...
Expansion and one-range addition theorems for complete orthonormal sets of spinor wave functions and Slater spinor orbitals of arbitrary half-integral spin in position, momentum and four-dimensional spaces
Exponential type spinor orbitals Slater type spinor orbitals Addition theorems
2010/12/9
The analytical relations in position, momentum and four-dimensional spaces are established
for the expansion and one-range addition theorems of relativistic complete orthonormal sets
of exponential ...
We study some properties of smooth sets in the sense defined by Hungerford ([2]). We prove a sharp form of Hungerford’s Theorem on the Hausdorff dimension of their boundaries on Euclidean spaces and s...