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math-ph2008★ 8 cited
Non-Haar -adic wavelets and their application to pseudo-differential operators and equations
A. Yu. Khrennikov, V. M. Shelkovich
In this paper a countable family of new compactly supported {\em non-Haar} -adic wavelet bases in ${\cL}^2(\bQ_p^n)$ is constructed. We use the wavelet bases in the following ap…
math-ph2008
Asymptotical behavior of one class of -adic singular Fourier integrals
A. Yu. Khrennikov, V. M. Shelkovich
We study the asymptotical behavior of the -adic singular Fourier integrals $$ J_{π_α,m;ϕ}(t) =\bigl< f_{π_α;m}(x)χ_p(xt), ϕ(x)\bigr> =F\big[f_{π_α;m}ϕ\big](t), \quad |t|_p \to \…
math.AP2008
A counter example on nontangential convergence for oscillatory integrals
Karoline Johansson
Consider the solution of the time-dependent Schr{ö}dinger equation with initial data . It is shown in \cite{artikel} that there exists in the Sobolev space $H^s(\RR), s=n/2$…