Related papers: Resonance index and singular mu-invariant

The construction of exactly solvable refractive indices allowing guided TE modes in optical waveguides is investigated within the formalism of Darboux-Crum transformations. We apply the finite-difference algorithm for higher-order…

We study the direct and inverse spectral problems for semiclassical operators of the form $S = S_0 +\h^2V$, where $S_0 = \frac 12 \Bigl(-\h^2\Delta_{\bbR^n} + |x|^2\Bigr)$ is the harmonic oscillator and $V:\bbR^n\to\bbR$ is a tempered…

Let $A$ be a $C^*$-algebra and $I$ be a closed ideal in $A$. For $x\in A$, its image under the canonical surjection $A\to A/I$ is denoted by $\dot x$, and the spectral radius of $x$ is denoted by $r(x)$. We prove that $$\max\{r(x), \|\dot…

We report the experimental realization of perfect sound absorption by sub-wavelength monopole and dipole resonators that exhibit degenerate resonant frequencies. This is achieved through the destructive interference of two resonators'…

In conventional model independent approaches, the power spectrum of primordial perturbations is characterized by such free parameters as spectral index, its running, the running of running, and the tensor-to-scalar ratio. In this work we,…

We produce a new proof and extend results by Harrell and Stubbe for the discrete spectrum of a self-adjoint operator. An abstract approach--based on commutator algebra, the Rayleigh-Ritz principle, and an ``optimal'' usage of the…

We extend the modular invariance property of the trace functions of vertex operator algebra on the set of irreducible modules (Zhu's theory) to the case of trace functions of intertwining operators.

We shall consider a double infinite, hermitian, complex entry matrix $A=[a_{x,y}]_{x,y\in\mathbb Z}$, with $a_{x,y}^*=a_{y,x}$, $x,y\in\mathbb Z$. Assuming that the matrix is almost of a finite bandwidth, i.e. there exists an integer $n> 0$…

Consider the inverse random source scattering problem for the two-dimensional time-harmonic elastic wave equation with an inhomogeneous, anisotropic mass density. The source is modeled as a microlocally isotropic generalized Gaussian random…

It is well known that the standard projection methods allow one to recover the whole spectrum of a bounded self-adjoint operator but they often lead to spectral pollution, i.e. to spurious eigenvalues lying in the gaps of the essential…

Motivated by applications to acoustic imaging, the present work establishes a framework to analyze scattering for the one-dimensional wave, Helmholtz, Schr\"odinger and Riccati equations that allows for coefficients which are more singular…

We consider a $2\times2$ block operator matrix ${\mathcal A}_\mu$ $($$\mu>0$ is a coupling constant$)$ acting in the direct sum of one- and two-particle subspaces of a bosonic Fock space. The location of the essential spectrum of ${\mathcal…

In (2+1)-dimensional general relativity, the path integral for a manifold $M$ can be expressed in terms of a topological invariant, the Ray-Singer torsion of a flat bundle over $M$. For some manifolds, this makes an explicit computation of…

A peculiar property of complex scattering potentials is the appearance of spectral singularities. These are energy eigenvalues for certain scattering states that similarly to resonance states have infinite reflection and transmission…

We revisit the concept of spectral averaging and point out its origin in connection with one-parameter subgroups of $SL_2(\bbR)$ and the corresponding M\"obius transformations. In particular, we identify exponential Herglotz representations…

In this paper, we explore spectral measures whose square integrable spaces admit a family of exponential functions as an orthonormal basis.Our approach involves utilizing the integral periodic zeros set of Fourier transform to characterize…

We study the perturbation of bound states embedded in the continuous spectrum which are unstable by the Fermi Golden Rule. The approach to resonance theory based on spectral deformation is extended to a more general class of quantum systems…

We introduce the concept of a \mu-scale invariant operator with respect to unitary transformation in a separable complex Hilbert space. We show that if a nonnegative densely defined symmetric operator is \mu-scale invariant for some \mu >0,…

Invariant coordinate selection is an unsupervised multivariate data transformation useful in many contexts such as outlier detection or clustering. It is based on the simultaneous diagonalization of two affine equivariant and positive…

Let the dimension $N$ of data and the sample size $T$ tend to $\infty$ with $N/T \to c > 0$. The spectral properties of a sample correlation matrix $\mathbf{C}$ and a sample covariance matrix $\mathbf{S}$ are asymptotically equal whenever…