Convolution operator on $ell^infty_{mathbb{Z}}$
Let $P_t colon ell^infty_mathbb{Z} to ell^infty_mathbb{Z}$ the map defined by
$$
widehat{P_t(f)}(xi)
=e^{-t sin pi xi}hat{f}(xi)
$$
where $f in ell^infty_{mathbb{Z}}$, where
$$
hat{f}(xi)
=sum_{x in mathbb{Z}} f(x)e^{2pi i xi x}
$$
and where $xi in mathbb{T}=[-1/2, 1/2)$. It is considered in the page 15 of the paper
https://arxiv.org/abs/1804.07679
I know that the map $P_t$ is a convolution operator $P_t(f)= f ast b_t$ by a sequence $b_t=(b_{t,n})_{n in mathbb{Z}}$. What is the sequence $b_t=(b_{t,n})_{n in mathbb{Z}}$ ?
functional-analysis fourier-analysis fourier-transform harmonic-analysis
asked Dec 11 '18 at 14:10
Zouba
903517
add a comment |
Let $P_t colon ell^infty_mathbb{Z} to ell^infty_mathbb{Z}$ the map defined by
$$
widehat{P_t(f)}(xi)
=e^{-t sin pi xi}hat{f}(xi)
$$
where $f in ell^infty_{mathbb{Z}}$, where
$$
hat{f}(xi)
=sum_{x in mathbb{Z}} f(x)e^{2pi i xi x}
$$
and where $xi in mathbb{T}=[-1/2, 1/2)$. It is considered in the page 15 of the paper
https://arxiv.org/abs/1804.07679
I know that the map $P_t$ is a convolution operator $P_t(f)= f ast b_t$ by a sequence $b_t=(b_{t,n})_{n in mathbb{Z}}$. What is the sequence $b_t=(b_{t,n})_{n in mathbb{Z}}$ ?
functional-analysis fourier-analysis fourier-transform harmonic-analysis
asked Dec 11 '18 at 14:10
Zouba
903517
add a comment |
Let $P_t colon ell^infty_mathbb{Z} to ell^infty_mathbb{Z}$ the map defined by
$$
widehat{P_t(f)}(xi)
=e^{-t sin pi xi}hat{f}(xi)
$$
where $f in ell^infty_{mathbb{Z}}$, where
$$
hat{f}(xi)
=sum_{x in mathbb{Z}} f(x)e^{2pi i xi x}
$$
and where $xi in mathbb{T}=[-1/2, 1/2)$. It is considered in the page 15 of the paper
https://arxiv.org/abs/1804.07679
I know that the map $P_t$ is a convolution operator $P_t(f)= f ast b_t$ by a sequence $b_t=(b_{t,n})_{n in mathbb{Z}}$. What is the sequence $b_t=(b_{t,n})_{n in mathbb{Z}}$ ?
functional-analysis fourier-analysis fourier-transform harmonic-analysis
asked Dec 11 '18 at 14:10
Zouba
903517
Let $P_t colon ell^infty_mathbb{Z} to ell^infty_mathbb{Z}$ the map defined by
$$
widehat{P_t(f)}(xi)
=e^{-t sin pi xi}hat{f}(xi)
$$
where $f in ell^infty_{mathbb{Z}}$, where
$$
hat{f}(xi)
=sum_{x in mathbb{Z}} f(x)e^{2pi i xi x}
$$
and where $xi in mathbb{T}=[-1/2, 1/2)$. It is considered in the page 15 of the paper
https://arxiv.org/abs/1804.07679
I know that the map $P_t$ is a convolution operator $P_t(f)= f ast b_t$ by a sequence $b_t=(b_{t,n})_{n in mathbb{Z}}$. What is the sequence $b_t=(b_{t,n})_{n in mathbb{Z}}$ ?
functional-analysis fourier-analysis fourier-transform harmonic-analysis
functional-analysis fourier-analysis fourier-transform harmonic-analysis
asked Dec 11 '18 at 14:10
Zouba
903517
asked Dec 11 '18 at 14:10
Zouba
903517
asked Dec 11 '18 at 14:10
Zouba
903517
asked Dec 11 '18 at 14:10
Zouba
903517
asked Dec 11 '18 at 14:10
Zouba
903517
903517
add a comment |
add a comment |
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