@@ -100,12 +100,26 @@ for T in (:CosSpace,:SinSpace)
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end
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"""
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- `CosSpace()` is the space spanned by `[1,cos θ,cos 2θ,...]`
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+ CosSpace()
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+ The space spanned by `[1, cos θ, cos 2θ, ...]`
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+
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+ ---
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+
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+ CosSpace(d::Domain)
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+
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+ The space spanned by `[1,cos(2pi/L*θ), cos(2pi/L*2θ), ...]` for a domain with a period `L`
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"""
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CosSpace ()
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"""
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- `SinSpace()` is the space spanned by `[sin θ,sin 2θ,...]`
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+ SinSpace()
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+ The space spanned by `[sin θ, sin 2θ, ...]`
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+
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+ ---
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+
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+ SinSpace(d::Domain)
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+
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+ The space spanned by `[1, sin(2pi/L*θ), sin(2pi/L*2θ), ...]` for a domain with a period `L`
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"""
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SinSpace ()
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@@ -301,11 +315,21 @@ evaluate(f::AbstractVector,S::SinSpace,t) = sineshaw(f,tocanonical(S,t))
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# # Laurent space
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"""
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- `Laurent()` is the space spanned by the complex exponentials
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+ Laurent()
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+ The space spanned by the complex exponentials
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```
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1,exp(-im*θ),exp(im*θ),exp(-2im*θ),…
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```
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- See also `Fourier`.
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+ See also [`Fourier`](@ref).
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+
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+ ---
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+
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+ Laurent(d::Domain)
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+ The space spanned by the complex exponentials
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+ ```
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+ 1, exp(-im * (2pi/L*θ)), exp(im * (2pi/L*θ)), exp(-2im * (2pi/L*θ)), …
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+ ```
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+ for a domain with a period `L`.
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"""
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const Laurent{DD,RR} = SumSpace{Tuple{Hardy{true ,DD,RR},Hardy{false ,DD,RR}},DD,RR}
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@@ -393,11 +417,21 @@ end
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# # Fourier space
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"""
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- `Fourier()` is the space spanned by the trigonemtric polynomials
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+ Fourier()
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+ The space spanned by the trigonemtric polynomials
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```
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- 1,sin(θ),cos(θ),sin(2θ),cos(2θ),…
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+ 1, sin(θ), cos(θ), sin(2θ), cos(2θ), …
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```
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See also `Laurent`.
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+
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+ ---
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+
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+ Fourier(d::Domain)
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+ The space spanned by the trigonemtric polynomials
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+ ```
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+ 1, sin(2pi/L*θ), cos(2pi/L*θ), sin(2pi/L*2θ), cos(2pi/L*2θ), …
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+ ```
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+ for a domain with a period `L`.
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"""
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const Fourier{DD,RR} = SumSpace{Tuple{CosSpace{DD,RR},SinSpace{DD,RR}},DD,RR}
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