Related papers: On the Ruelle eigenvalue sequence
There exist conjectural formulas on relations between $L$-functions of submotives of Shimura varieties and automorphic representations of the corresponding reductive groups, due to Langlands -- Arthur. In the present paper these formulas…
We show that the interior transmission eigenvalues are discrete by proving that the interior transmission operator has upper triangular compact resolvent, and that the spectrum of these operators share many of the properties of operators…
In this paper, we consider a discontinuous Dirac operator with eigenparameter dependent both boundary and two transmission conditions. We introduce a suitable Hilbert space formulation and get some properties of eigenvalues and…
In the present work we study existence of sequences of variational eigenvalues to non-local non-standard growth problems ruled by the fractional $g-$Laplacian operator with different boundary conditions (Dirichlet, Neumann and Robin). Due…
In this article, we obtain some results in the direction of ``infinite dimensional symplectic spectral theory". We prove an inequality between the eigenvalues and symplectic eigenvalues of a special class of infinite dimensional operators.…
We show that spectral data of transfer operators given by holomorphic data can be approximated using an effective numerical scheme based on Lagrange interpolation. In particular, we show that for one-dimensional systems satisfying certain…
Regular Sturm-Liouville problems with indefinite weight functions may possess finitely many non-real eigenvalues. In this note we prove explicit bounds on the real and imaginary parts of these eigenvalues in terms of the coefficients of the…
In this paper, we consider eigenvalues of the Dirichlet biharmonic operator on a bounded domain in a hyperbolic space. We obtain universal bounds on the $(k+1)$th eigenvalue in terms of the first $k$th eigenvalue independent of the domains.
A systematic exposition is given of the theory of invariant differential operators on a not necessarily reductive homogeneous space. This exposition is modelled on Helgason's treatment of the general reductive case and the special…
We show how eigenvalue estimates for linear operators can be used to obtain new Blaschke type bounds on zeros of holomorphic functions on the unit disk.
We study boundary value problems for some differential operators on Euclidean space and the Heisenberg group which are invariant under the conformal group of a Euclidean subspace resp. Heisenberg subgroup. These operators are shown to be…
We consider the eigenvalues of an elliptic operator for systems with bounded, measurable, and symmetric coefficients. We assume we have two non-empty, open, disjoint, and bounded sets and add a set of small measure to form the perturbed…
Based on empirical evidence, quantum systems appear to be strictly linear and gauge invariant. This work uses concise mathematics to show that quantum eigenvalue equations on a one dimensional ring can either be gauge invariant or have a…
In this note we investigate the operators associated with frame sequences in a Hilbert space $H$, i.e., the synthesis operator $T:\ell ^{2}(\mathbb{N}) \to H$, the analysis operator $T^{\ast}:H\to $ $% \ell ^{2}(\mathbb{N}) $ and the…
Long Range Dependence (LRD) in functional sequences is characterized in the spectral domain under suitable conditions. Particularly, multifractionally integrated functional autoregressive moving averages processes can be introduced in this…
We estimate the eigenvalues of connection Laplacians in terms of the non-triviality of the holonomy.
We consider self-similar measures on $\mathbb R.$ The Hutchinson operator $H$ acts on measures and is the dual of the transfer operator $T$ which acts on continuous functions. We determine polynomial eigenfunctions of $T .$ As a…
The scaling behavior of the SO(3) irreducible amplitudes $d_n^l(r)$ of velocity structure tensors (see L'vov, Podivilov, and Procaccia, Phys. Rev. Lett. (1997)) is numerically examined for Navier-Stokes turbulence. Here, l characterizes the…
We study an eigenvalue problem involving a degenerate and singular elliptic operator on the whole space $\mathbb{R}^N$. We prove the existence of an unbounded and increasing sequence of eigenvalues. Our study generalizes to the case of…
We study the spectral properties of curl, a linear differential operator of first order acting on differential forms of appropriate degree on an odd-dimensional closed oriented Riemannian manifold. In three dimensions its eigenvalues are…