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For idle curiosity....if I have some unknown functions f,g,h but I know their convolutions f*g, g*h, and f*h, is this enough information to figure out what f,g,h are? If not, what additional information is needed to pin them down? -- HappyCamper 12:53, 25 May 2019 (UTC)
Given any function f from the real numbers R to itself, a period of f is any real number p for which f(x + p) = f(x) for all real numbers x. Clearly, the periods of any function (including zero) always form a subgroup of the additive group of real numbers. For which subgroups G of (R, +) does there exist a continuous function f for which the subgroup of periods of f is exactly equal to G? Note that if continuity is not required, then such a function always exists: just let f be the indicator function of G. GeoffreyT2000 ( talk) 14:24, 25 May 2019 (UTC)
Mathematics desk | ||
---|---|---|
< May 24 | << Apr | May | Jun >> | Current desk > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is a transcluded archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
For idle curiosity....if I have some unknown functions f,g,h but I know their convolutions f*g, g*h, and f*h, is this enough information to figure out what f,g,h are? If not, what additional information is needed to pin them down? -- HappyCamper 12:53, 25 May 2019 (UTC)
Given any function f from the real numbers R to itself, a period of f is any real number p for which f(x + p) = f(x) for all real numbers x. Clearly, the periods of any function (including zero) always form a subgroup of the additive group of real numbers. For which subgroups G of (R, +) does there exist a continuous function f for which the subgroup of periods of f is exactly equal to G? Note that if continuity is not required, then such a function always exists: just let f be the indicator function of G. GeoffreyT2000 ( talk) 14:24, 25 May 2019 (UTC)