Related papers: Scales in the Point Spectrum
We prove non-trivial upper and lower bounds for the "Spectrum of Singularities" of Fourier Series with polynomial frequencies. The Spectrum of Singularities of a function f gives the Hausdorff dimension of the set of points with a given…
We discuss the possible applications supersymmetric theories might find in the field of elementary particle physics. The supersymmetric generalization of the $SU(3)\times SU(2)\times U(1)$ standard model is discussed in detail. Special…
This paper establishes an upper bound on the number of generalized cospectral mates of simple graphs, where the generalized spectrum consists of the spectrum of a graph and its complement. Moving beyond the classical problem of identifying…
We study properties of strongly separately continuous mappings defined on subsets of products of topological spaces equipped with the topology of pointwise convergence. In particular, we give a necessary and sufficient condition for a…
We construct a map from the suspension $G$-spectrum $\Sigma_G^\infty M$ of a smooth compact $G$-manifold to the equivariant $A$-theory spectrum $A_G(M)$, and we show that its fiber is, on fixed points, a wedge of stable $h$-cobordism…
We consider the uniqueness of solutions of ordinary differential equations where the coefficients may have singularities. We derive upper bounds on the the order of singularities of the coefficients and provide examples to illustrate the…
We prove bounds for a class of unital homomorphisms arising in the study of spectral sets, by involving extremal functions and vectors. These are used to recover three celebrated results on spectral constants by Crouzeix--Palencia,…
The search for a highly discriminating and easily computable invariant to distinguish graphs remains a challenging research topic. Here we focus on cospectral graphs whose complements are also cospectral (generalized cospectral), and on…
We develop a theory of R-module Thom spectra for a commutative symmetric ring spectrum R and we analyze their multiplicative properties. As an interesting source of examples, we show that R-algebra Thom spectra associated to the special…
We establish spectral estimates at a critical energy level for $h$-pseudors . Via a trace formula, we compute the contribution of isolated (non-extremum) critical points under a condition of "real principal type". The main result holds for…
First we study the spectral singularity at infinity and investigate the connections of the spectral singularities and the spectrality of the Hill operator. Then we consider the spectral expansion when there is not the spectral singularity…
Consider a conformally covariant four-point function of identical scalar operators with a discrete spectrum, a twist gap, and compatible with the unitarity conditions. We give a mathematical proof confirming that the spectrum and OPE…
We study the critical properties of the monopole-percolation transition in U(1) lattice gauge theory coupled to scalars at infinite ($\beta=0$) gauge coupling. We find strong scaling corrections in the critical exponents that must be…
In this article we prove a generalization of Weyl's criterion for the spectrum of a self-adjoint nonnegative operator on a Hilbert space. We will apply this new criterion in combination with Cheeger-Fukaya-Gromov and Cheeger-Colding theory…
We show the relevance of a multifractal-type analysis for pointwise convergence and divergence properties of wavelet series: Depending on the sequence space which the wavelet coefficients sequence belongs to, we obtain deterministic upper…
The scaling behaviour of the diffraction intensity near the origin is investigated for (partially) ordered systems, with an emphasis on illustrative, rigorous results. This is an established method to detect and quantify the fluctuation…
Results regarding probable bifurcations from fixed points are presented in the context of general dynamical systems (real, random matrices), time-delay dynamical systems (companion matrices), and a set of mappings known for their properties…
A Transposition graph $T_n$ is defined as a Cayley graph over the symmetric group $Sym_n$ generated by all transpositions. This paper shows how the spectrum of $T_n$ can be obtained using the spectral properties of the Jucys-Murphy…
Spectral measures arise in numerous applications such as quantum mechanics, signal processing, resonances, and fluid stability. Similarly, spectral decompositions (pure point, absolutely continuous and singular continuous) often…
Exceptional points are found in the spectrum of a prototypical thermoacoustic system as the parameters of the flame transfer function are varied. At these points, two eigenvalues and the associated eigenfunctions coalesce. The system's…