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Statements

Subject Item
dbr:Conjugate_Fourier_series
rdfs:label
Conjugate Fourier series
rdfs:comment
In the mathematical field of Fourier analysis, the conjugate Fourier series arises by realizing the Fourier series formally as the boundary values of the real part of a holomorphic function on the unit disc. The imaginary part of that function then defines the conjugate series. studied the delicate questions of convergence of this series, and its relationship with the Hilbert transform. In detail, consider a trigonometric series of the form in which the coefficients an and bn are real numbers. This series is the real part of the power series
dcterms:subject
dbc:Fourier_analysis dbc:Fourier_series
dbo:wikiPageID
17404231
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1085144676
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dbr:Unit_circle dbr:Imaginary_part dbr:Mathematics dbr:Unit_disc dbr:Fourier_analysis dbr:Holomorphic_function dbr:Trigonometric_series dbc:Fourier_series dbr:Power_series dbr:Real_number dbr:Hilbert_transform dbr:Real_part dbc:Fourier_analysis dbr:Harmonic_conjugate dbr:Springer-Verlag
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dbo:abstract
In the mathematical field of Fourier analysis, the conjugate Fourier series arises by realizing the Fourier series formally as the boundary values of the real part of a holomorphic function on the unit disc. The imaginary part of that function then defines the conjugate series. studied the delicate questions of convergence of this series, and its relationship with the Hilbert transform. In detail, consider a trigonometric series of the form in which the coefficients an and bn are real numbers. This series is the real part of the power series along the unit circle with . The imaginary part of F(z) is called the conjugate series of f, and is denoted
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wikipedia-en:Conjugate_Fourier_series?oldid=1085144676&ns=0
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1777
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wikipedia-en:Conjugate_Fourier_series