page_title: Strömberg wavelet
section_title: Strömberg wavelets of order 0
hierarchical_section_title: Strömberg wavelet / Strömberg wavelets of order 0
caption_attribution_description: English: The graph of the Stromberg wavelet of order 0. The graph is scaled such that the value of the wavelet function at 1 is 1.
context_page_description: In mathematics, the Strömberg wavelet is a certain orthonormal wavelet discovered by Jan-Olov Strömberg and presented in a paper published in 1983. Even though the Haar wavelet was earlier known to be an orthonormal wavelet, Stromberg wavelet was the first smooth orthonormal wavelet to be discovered. The term wavelet had not been coined at the time of publishing the discovery of Strömberg wavelet and Strömberg's motivation was to find an orthonormal basis for the Hardy spaces.
context_section_description: In the special case of Strömberg wavelets of order 0, the following facts may be observed:
  If f(t) ∈ P⁰(V) then f(t) is defined uniquely by the discrete subset {f(r) : r ∈ V} of R.
  To each s ∈ A₀, a special function λₛ in A₀ is associated: It is defined by λₛ(r) = 1 if r = s and λₛ(r) = 0 if  s ≠ r ∈ A₀. These special elements in P(A₀) are called simple tents. The special simple tent λ1/2(t) is denoted by λ(t)
caption: The graph of the Strömberg wavelet of order 0. The graph is scaled such that the value of the wavelet function at 1 is 1.
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