|
In mathematics, the Weyl integral is an operator defined, as an example of fractional calculus, on functions ''f'' on the unit circle having integral 0 and a Fourier series. In other words there is a Fourier series for ''f'' of the form : with ''a''0 = 0. Then the Weyl integral operator of order ''s'' is defined on Fourier series by : where this is defined. Here ''s'' can take any real value, and for integer values ''k'' of ''s'' the series expansion is the expected ''k''-th derivative, if ''k'' > 0, or (−''k'')th indefinite integral normalized by integration from ''θ'' = 0. The condition ''a''0 = 0 here plays the obvious role of excluding the need to consider division by zero. The definition is due to Hermann Weyl (1917). ==See also== *Sobolev space 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Weyl integral」の詳細全文を読む スポンサード リンク
|