Talk:Carleman matrix

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[edit] Categorical interpretation

The section about the categorical interpretation of the Carleman matrix doesn't make sense to me. What would an analytic function on an arbitrary set be? How does one multiply arbitrary infinite matrices (to form the proposed category VecInf)? What is the operation of the supposed Carleman functor on objects? Most important, is there a reference for this to a reliable source? -- Spireguy (talk) 23:42, 13 May 2008 (UTC)

[edit] The Carleman-concept only meaningful for functions defined by powerseries

Thinking about the carleman-matrices, and especially the transformation of a function-iteration into matrix-multiplication. If f is, say a zeta-series, how could an iteration be thought? Assume the carleman-matrix for the zeta-function z(s). We may have correctly created the carlemanmatrix Z. Then we have something using derivatives of z(s) the sum of some powers of x by the derivatives of z some function g(x), maybe this is then zeta(x) Them using the next rows gives g(x)^2, g(x)^3,... and we are in the concept of powerseries. In the next iteration, we have then powers of x by powers of g(x) - and I don't belive this is anything related to an iteration of the zeta-series.

Thus - by this sketch I question, if it should be mentioned, that the carleman-concept with its matrix-power-method is meaningful only for function, expressed as polynomials and powerseries in x.

Opinions? Gotti 10:56, 8 June 2008 (UTC)