Sextic reciprocal monogenic dihedral polynomials
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DOI: 10.1007/s11139-020-00310-w
Abstract: Let $$D_n$$ denote the dihedral group of order 2n. We find infinite $$D_6$$ -families and an infinite $$D_3$$ -family of monic irreducible reciprocal sixth-degree polynomials $$f(x)\in \mathbb {Z}[x]$$ , such that $$\{1,\theta ,\theta ^2,\theta ^3,\theta… read more here.
Keywords: dihedral polynomials; theta theta; theta; reciprocal monogenic ... See more keywords
Ranks of Cross-Commutators and Unitary Module Maps
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DOI: 10.1007/s40315-018-0239-1
Abstract: Let M be an invariant subspace of $$H^2$$H2 over the bi-disk and $$N=H^2\ominus M$$N=H2⊖M. Let $$S_{z,N},S_{w,N}$$Sz,N,Sw,N be the compression of the multiplication operators $$T_z,T_w$$Tz,Tw on $$H^2$$H2 onto N. For a two-variable inner function $$\theta $$θ,… read more here.
Keywords: ranks cross; theta theta; theta; unitary module ... See more keywords
The Variance of the Number of Zeros for Complex Random Polynomials Spanned by OPUC
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DOI: 10.1007/s40315-020-00305-0
Abstract: Let $$\{\varphi _k\}_{k=0}^\infty $$ { φ k } k = 0 ∞ be a sequence of orthonormal polynomials on the unit circle with respect to a probability measure $$ \mu $$ μ . We study… read more here.
Keywords: variance number; number zeros; theta; theta theta ... See more keywords
Uniform resolvent estimates for Schrödinger operator with an inverse-square potential
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DOI: 10.1016/j.jfa.2019.108350
Abstract: We study the uniform resolvent estimates for the Schrodinger operator with a Hardy-type singular potential. Let $\mathcal{L}_V=-\Delta+V(x)$ where $\Delta$ is the usual Laplacian on $\mathbb{R}^n$ and $V(x)=V_0(\theta) r^{-2}$ where $r=|x|, \theta=x/|x|$ and $V_0(\theta)\in\mathcal{C}^1(\mathbb{S}^{n-1})$ is a… read more here.
Keywords: operator; uniform resolvent; theta theta; resolvent estimates ... See more keywords
Bounds on the dynamics of periodic quantum walks and emergence of the gapless and gapped Dirac equation
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DOI: 10.1103/physreva.97.012116
Abstract: We study the dynamics of discrete-time quantum walk using quantum coin operations, $\hat{C}(\theta_1)$ and $\hat{C}(\theta_2)$ in time-dependent periodic sequence. For the two-period quantum walk with the parameters $\theta_1$ and $\theta_2$ in the coin operations we… read more here.
Keywords: theta theta; quantum walks; theta; period quantum ... See more keywords