08/30/2009, 10:19 PM
Hi,
I was wondering.... If all the various forms of tetration that grow faster than exponential at as x-> infinity are Fourier transformed, they should have an extra high frequency peak(s) representing that extra speed as Fourief multiplier can not damp it at same value.
1) Would it be than possible to order all various tetrations ( finite right, left, mixed, infinite versions) by their Fourier spectra or even peak frequencies, making classification easier?
2) Since a pulse is usually depicted as Heaviside function, or delta function, with infinite growth speed of front, and, since it is known that no discontinuity can propagate faster than light, for modeling of real life pulses moving via systems could we use tetration approximations to the front? Such front can have any speed > c ( since it will represent phase or group speed) and, for a given (even linear) system, one could perhaps create a tetration ( or higher) front that propagates with any given speed?
3) Can we have a mathematical pulse with backward leaning front where top of pulse enters system before the bottom- so to say, the signal front is negative?
Ivars
I was wondering.... If all the various forms of tetration that grow faster than exponential at as x-> infinity are Fourier transformed, they should have an extra high frequency peak(s) representing that extra speed as Fourief multiplier can not damp it at same value.
1) Would it be than possible to order all various tetrations ( finite right, left, mixed, infinite versions) by their Fourier spectra or even peak frequencies, making classification easier?
2) Since a pulse is usually depicted as Heaviside function, or delta function, with infinite growth speed of front, and, since it is known that no discontinuity can propagate faster than light, for modeling of real life pulses moving via systems could we use tetration approximations to the front? Such front can have any speed > c ( since it will represent phase or group speed) and, for a given (even linear) system, one could perhaps create a tetration ( or higher) front that propagates with any given speed?
3) Can we have a mathematical pulse with backward leaning front where top of pulse enters system before the bottom- so to say, the signal front is negative?
Ivars