Browsing Mathematics by Subject "math.SP"
Now showing items 1-9 of 9
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Critical Gagliardo-Nirenberg, Trudinger, Brezis-Gallouet-Wainger inequalities on graded groups and ground states
In this paper we investigate critical Gagliardo-Nirenberg, Trudinger-type and Brezis-Gallouet-Wainger inequalities associated with the positive Rockland operators on graded groups, which includes the cases of $\mathbb R^n$, ... -
Eigenfunction expansions of ultradifferentiable functions and ultradistributions. III. Hilbert spaces and Universality
(Springer, 2021-03)In this paper we analyse the structure of the spaces of smooth type functions, generated by elements of arbitrary Hilbert spaces, as a continuation of the research in our previous papers in this series. We prove that these ... -
Hardy inequalities on metric measure spaces, II: The case $p>q$
In this note we continue giving the characterisation of weights for two-weight Hardy inequalities to hold on general metric measure spaces possessing polar decompositions. Since there may be no differentiable structure on ... -
Harmonic and Anharmonic Oscillators on the Heisenberg Group
(Elsevier, 2021-05-25)Although there is no canonical version of the harmonic oscillator on the Heisenberg group $\mathbf{H}_n$ so far, we make a strong case for a particular choice of operator by using the representation theory of the Dynin-Folland ... -
Hybrid sup-norm bounds for Maass newforms of powerful level
(Mathematical Sciences Publishers, 2017-07-12)Let $f$ be an $L^2$-normalized Hecke--Maass cuspidal newform of level $N$, character $\chi$ and Laplace eigenvalue $\lambda$. Let $N_1$ denote the smallest integer such that $N|N_1^2$ and $N_0$ denote the largest integer ... -
Localization and landscape functions on quantum graphs
We discuss explicit landscape functions for quantum graphs. By a "landscape function" $\Upsilon(x)$ we mean a function that controls the localization properties of normalized eigenfunctions $\psi(x)$ through a pointwise ... -
On Agmon metrics and exponential localization for quantum graphs
(Springer Verlag, 2018-03-28)We investigate the rate of decrease at infinity of eigenfunctions of quantum graphs by using Agmon's method to prove $L^2$ and $L^\infty$ bounds on the product of an eigenfunction with the exponential of a certain metric. ... -
Schatten-von Neumann classes of integral operators
(Elsevier, 2021)In this work we establish sharp kernel conditions ensuring that the corresponding integral operators belong to Schatten-von Neumann classes. The conditions are given in terms of the spectral properties of operators acting ... -
Sup-norms of eigenfunctions in the level aspect for compact arithmetic surfaces
(Springer (part of Springer Nature), 2019-11-01)Let $D$ be an indefinite quaternion division algebra over $\mathbb{Q}$. We approach the problem of bounding the sup-norms of automorphic forms $\phi$ on $D^\times(\mathbb{A})$ that belong to irreducible automorphic ...