On my old fractional calculus approach to hyper-operations
#12
Man, I guess I'm supposed to understand that integral formula but I can't. Can you elaborate a little bit? That K function confuses me.

About iterating kernels... If you read my story about ranks what I'm doing, in some sense, is iterating a kind of kernel.
And the kernel is a pre-image under the matrix so iterating kernel is iterating matrix even without the eigen-theory "bologna" xD..

Edit. To be clear if \( f\mapsto \Sigma_s(f)=fsf^{-1} \) is the operator the "kernels" are \( f\mapsto [s,f] \). Do you remember when you were telling me that that operator "it is not as well defined as you think" back in 2014?
It is like indefinite integral (antiderivative). It is a pre-image inverse to differentiation. The same way we define pre-images and kernels.

Mother Law \(\sigma^+\circ 0=\sigma \circ \sigma^+ \)

\({\rm Grp}_{\rm pt} ({\rm RK}J,G)\cong \mathbb N{\rm Set}_{\rm pt} (J, \Sigma^G)\)
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RE: On my old fractional calculus approach to hyper-operations - by MphLee - 05/28/2021, 10:58 PM

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