We prove that supports of a wide class temperate distributions with uniformly discrete support and spectrum on Euclidean spaces are finite unions translations full-rank lattices. This result is generalization the corresponding theorem for Fourier quasicrystals, its proof uses technique almost periodic distributions.

The spectrum of a finite group is the set element orders this group. main goal paper to survey results concerning recognition simple groups by spectrum, in particular, list all for which problem solved.

This paper arose from attempting to understand Bousfield localization functors in stable homotopy theory. All spectra will be p-local for a prime p throughout this paper. Recall that if E is a spectrum, a spectrum X is E-acyclic if E ∧X is null. A spectrum is E-local if every map from an E-acyclic spectrum to it is null. A map X → Y is an E-equivalence if it induces an isomorphism on E∗, or equ...

“Weyl’s theorem holds” for an operator T on a Banach space X when the complement in the spectrum of the “Weyl spectrum” coincides with the isolated points of spectrum which are eigenvalues of finite multiplicity. This is close to, but not quite the same as, equality between the Weyl spectrum and the “Browder spectrum”, which in turn ought to, but does not, guarantee the spectral mapping theorem...

This paper arose from attempting to understand Bousfield localization functors in stable homotopy theory. All spectra will be p-local for a prime p throughout this paper. Recall that if E is a spectrum, a spectrum X is Eacyclic if E∧X is null. A spectrum is E-local if every map from an E-acyclic spectrum to it is null. A map X → Y is an E-equivalence if it induces an isomorphism on E∗, or equiv...

To a topological group G, we assign a naive G-spectrum DG, called the dualizing spectrum of G. When the classifying space BG is finitely dominated, we show that DG detects Poincaré duality in the sense that BG is a Poincaré duality space if and only ifDG is a homotopy finite spectrum. Secondly, we show that the dualizing spectrum behavesmultiplicatively on certain topological group extensions. ...

We investigate the spectrum of the differential operator Lλ defined by the Klein-Gordon s-wave equation y′′ +(λ−q(x))2y = 0, x ∈R+ = [0,∞), subject to the spectral parameterdependent boundary condition y′(0)−(aλ+b)y(0)= 0 in the space L(R+), where a≠±i, b are complex constants, q is a complex-valued function. Discussing the spectrum, we prove that Lλ has a finite number of eigenvalues and spect...

The interplay between between gauge-field winding numbers, θ-vacua, and the Dirac operator spectrum in finite-volume gauge theories is reconsidered. To assess the weight of each topological sector, we compare the mass-dependent chiral condensate in gauge field sectors of fixed topological index with the answer obtained by summing over the topological charge. Also the microscopic Dirac operator ...