arXiv subjects
Publications and source records attributed to Károly Nagy.
As main result we prove that Fejér means of Walsh-Kaczmarz-Fourier series are uniformly bounded operators from the Hardy martingale space $\ H_{p}$ to the Hardy martingale space $H_{p}$ for $ 0<p\leq 1/2.$
Chen and Hsiao gave the numerical solution of initial value problems of systems of linear differential equations with constant coefficients by Walsh polynomials approach. This result was improved by Gát and Toledo for initial value problems of differential equations with variable coefficients on the interval $[0,1[$ and initial value $ξ=0$. In the present paper we discuss the general case while $ξ$ can take any arbitrary value in the interval $[0,1[$. We show the existence and uniform convergence of the numerical solution, as well.
The properties of the maximal operator of the $(C,α)$-means ($α=(α_1,\ldots,α_d)$) of the multi-dimensional Walsh-Kaczmarz-Fourier series are discussed, where the set of indices is inside a cone-like set. We prove that the maximal operator is bounded from $H_p^γ$ to $L_p$ for $p_0< p $ ($p_0=\max{1/(1+α_k): k=1,\ldots, d}$) and is of weak type $(1,1)$. As a corollary we get the theorem of Simon \cite{S1} on the a.e. convergence of cone-restricted two-dimensional Fejér means of integrable functions. At the endpoint case $p=p_0$, we show that the maximal operator $σ^{κ,α,*}_L$ is not bounded from the Hardy space $H_{p_0}^γ$ to the space $L_{p_0}$.
Black phosphorus has emerged as the next member in the graphene inspired two-dimensional materials family. Its electronic and magnetic properties are studied herein using electron and nuclear magnetic resonance techniques (ESR and NMR) and microwave conductivity measurement. The latter is a unique technique to study conductivity on air sensitive samples. The ESR study indicates the absence of free charge carriers and no sign of paramagnetic defects are found. $^{31}$P NMR shows the presence of a characteristic Pake doublet structure due to the interaction between $I = 1/2$ nuclei. Microwave conductivity shows, in accordance with the ESR results, that black phosphorus behaves as a semiconductor and we identify extrinsic and intrinsic charge carrier contributions to the conductivity and extracted the sizes of the gaps. ESR measurement also yields that bP might find applications as a microwave absorbent.