Boundedness of Fourier transforms for Battle-Lemarie wavelets

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Let $phi$ and $psi$ be the scaling function and wavelet for the Battle-Lemarie wavelet of order $n$. Is it true that
$$
sup_x in mathbbR |hatphi(x)| < infty,
$$
$$
sup_x in mathbbR |hatpsi(x)| < infty,
$$
$$
sup_x in mathbbR |(hatpsi(x))'| < infty?
$$
(Hat denotes the Fourier transform in $L_2(R)$.) Or are these inequalities true at least for all $n > N$?




fourier-analysis fourier-transform harmonic-analysis wavelets




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    Let $phi$ and $psi$ be the scaling function and wavelet for the Battle-Lemarie wavelet of order $n$. Is it true that
    $$
    sup_x in mathbbR |hatphi(x)| < infty,
    $$
    $$
    sup_x in mathbbR |hatpsi(x)| < infty,
    $$
    $$
    sup_x in mathbbR |(hatpsi(x))'| < infty?
    $$
    (Hat denotes the Fourier transform in $L_2(R)$.) Or are these inequalities true at least for all $n > N$?




    fourier-analysis fourier-transform harmonic-analysis wavelets




    share|cite|improve this question





















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      Let $phi$ and $psi$ be the scaling function and wavelet for the Battle-Lemarie wavelet of order $n$. Is it true that
      $$
      sup_x in mathbbR |hatphi(x)| < infty,
      $$
      $$
      sup_x in mathbbR |hatpsi(x)| < infty,
      $$
      $$
      sup_x in mathbbR |(hatpsi(x))'| < infty?
      $$
      (Hat denotes the Fourier transform in $L_2(R)$.) Or are these inequalities true at least for all $n > N$?




      fourier-analysis fourier-transform harmonic-analysis wavelets




      share|cite|improve this question











      Let $phi$ and $psi$ be the scaling function and wavelet for the Battle-Lemarie wavelet of order $n$. Is it true that
      $$
      sup_x in mathbbR |hatphi(x)| < infty,
      $$
      $$
      sup_x in mathbbR |hatpsi(x)| < infty,
      $$
      $$
      sup_x in mathbbR |(hatpsi(x))'| < infty?
      $$
      (Hat denotes the Fourier transform in $L_2(R)$.) Or are these inequalities true at least for all $n > N$?





      fourier-analysis fourier-transform harmonic-analysis wavelets





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      share|cite|improve this question




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      asked Jul 16 at 8:25









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