Did you see that as a continuation of a stepwise function or to use your analogy, or were you in that case drafting things for the first time on paper?
According to statement (2), analytic fractal continuation of an analytic function is unique, not depending on the string θ ∈ Ω, and is the standard analytic continuation.
By continuation with zero of a function u ∈ X T to [ − T 1, T 1 ], we have X T ⊂ X T 1 and Γ T ⊂ Γ T 1.
This is because hyperfunction is a continuation of develop-mental function, not a random process.
I already mentioned progressive loss of fertility and menopause in women, which is a direct continuation of reproductive function.
A patient with total brain failure meets none of these criteria, even if a respirator permits the continuation of cardiopulmonary function.
Billingsley ( 1995 ) proved the implication that (hb) ⇒ (h8) by a version of analytic continuation of characteristic function, but it is easy to see that (hb) also implies (h7) and hence X is M-det on ({mathbb {R}}.) In Theorem 1, Carleman's condition (h7) is the weakest checkable condition for X to be M-det on ({mathbb {R}}).
Fractal continuation of such functions, an analog to classical analytic continuation, is the subject of Sect.
This proves the analytic continuation of the function s ↦ ζ ∗ ( s, α ; x ) as an entire function to the whole complex plane, except simple poles at s = α − n, 0 ≤ n < [ a ] if ℜ ≥ 1.
This proves the analytic continuation of the function s ↦ ζ ( s, α ; x, λ ) as an entire function to the whole complex plane, and Γ E m ( x ; − λ ) = 2 α ζ ( − m, α ; x, λ ).
