A new Pythagorean functional equation |
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| Authors: | H Haruki |
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| Institution: | 1. Department of Pure Mathematics, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada
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| Abstract: | The purpose of this paper is to solve the following Pythagorean functional equation:(e
p(x,y)
)
2
) = q(x,y)
2
+ r(x, y)
2, where each ofp(x,y), q(x, y) andr(x, y) is a real-valued unknown harmonic function of the real variablesx, y on the wholexy-planeR
2.The result is as follows. |
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| Keywords: | AMS (1980) subject classification" target="_blank">AMS (1980) subject classification Primary 35B40 Secondary 30D05 |
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