Harmonic entropy: Difference between revisions

Mike Battaglia (talk | contribs)
Mike Battaglia (talk | contribs)
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<math>\displaystyle \left[S \ast K\right]^a(-c)</math>
<math>\displaystyle \left[S \ast K\right]^a(-c)</math>


represents the convolution of <math>S</math> and <nowiki></math></nowiki>K, taken to the <math>a</math>'th power, and flipped backwards. Note that if <math>S(x)</math> is a symmetrical (even) spreading function, and if for each ratio <math>n/d</math> in <math>J</math>, if the inverse <math>d/n</math> is also in <math>J</math>, then the above convolution will also be symmetrical, and we also have
represents the convolution of <math>S</math> and <math>K</math>, taken to the <math>a</math>'th power, and flipped backwards. Note that if <math>S(x)</math> is a symmetrical (even) spreading function, and if for each ratio <math>n/d</math> in <math>J</math>, if the inverse <math>d/n</math> is also in <math>J</math>, then the above convolution will also be symmetrical, and we also have


<math>\displaystyle \left[S \ast K\right]^a(-c) = \left[S \ast K\right]^a(c)</math>
<math>\displaystyle \left[S \ast K\right]^a(-c) = \left[S \ast K\right]^a(c)</math>