Get Analysis in Positive Characteristic PDF

By Anatoly N. Kochubei

ISBN-10: 0511517777

ISBN-13: 9780511517778

ISBN-10: 0521509777

ISBN-13: 9780521509770

Dedicated to opposite numbers of classical buildings of mathematical research in research over neighborhood fields of confident attribute, this booklet treats confident attribute phenomena from an analytic perspective. development at the uncomplicated items brought by means of L. Carlitz - resembling the Carlitz factorials, exponential and logarithm, and the orthonormal procedure of Carlitz polynomials - the writer develops one of those differential and crucial calculi.

Show description

Read or Download Analysis in Positive Characteristic PDF

Similar analysis books

Download PDF by Thomas Kaiserfeld: Beyond Innovation: Technology, Institution and Change as

Past Innovation counter weighs the current innovation monomania through broadening our pondering technological and institutional switch. it's performed by means of a multidisciplinary assessment of the commonest principles concerning the dynamics among know-how and associations.

Read e-book online Failed Anti-Reflux Therapy: Analysis of Causes and PDF

This multiauthored textual content presents info at the pathophysiology of GERD, applicable scientific administration, and correct symptoms for and function of surgical and endoscopic strategies for GERD. hundreds of thousands of sufferers will event insufficient reduction from scientific treatment or will strengthen problems from their systems or recurrent or new signs afterwards; this article describes intimately the right kind assessment and administration of such sufferers.

Additional resources for Analysis in Positive Characteristic

Example text

First we prove that the sequence {|cn |q n } is bounded. Assuming the opposite, we find a strictly increasing sequence {nr } such that lim |cnr |q nr = ∞. Choosing, if necessary, an appropriate subsequence, we r→∞ may assume, for 0 ≤ n < nr , that |cn |q n < |cnr |q nr . 6) Suppose that u (0) = λ. 54) that t−1 fn (t) = gqn −1 (t) , Ln n = 0, 1, 2, . . 7) have the same roots t = xl , l < n, the same degrees and the same leading coefficients). 7), nr lim ϕ(xnr ) = lim r→∞ r→∞ cn gqn −1 (xnr ) = λ. 14) of the Carlitz polynomials, we find that gqn −1 (xn ) = Ln Dn n (−1)n−j j=0 n (qj −1)n x j n (−1)n−j = (−1)n + j=1 Ln j Dj Lqn−j where Ln j Dj Lqn−j = q −mn , x(q j −1)n 50 Chapter 2 mn = n + (q j − 1)n − qj − 1 − q j (n − j) = jq j − (1 + q + · · · + q j−1 ) > 0, q−1 so that gqn −1 (xn ) ≡ (−1)n (mod x).

The fact that the function t−1 γ(t) is continuous at t = 0 means that γ(t) is differentiable at t = 0. 2, |γn |q n → 0 for n → ∞. 11) with wn = L−1 n γn , so that wn → 0. Now we are in a position to prove the characterization result. 5 The function u = n=0 C0k+1 (O, K c ) if and only if k q nq |cn | → 0 for n → ∞. 13) In this case k sup |Dk u(t)| = sup q (n−k)q |cn |. 14) n≥k Proof. We use the identity fn−k , if n ≥ k, 0, if n < k. 15) n=k which implies the identity D u(t) k q −k ∞ −k cqn = n=k gqn−k −1 (t) , Ln−k t = 0.

Let u ∈ C0 (O, K c ), Dk u(t) = t−q ∆(k) u(t), k t ∈ O \ {0}. We will say that u ∈ C0k+1 (O, K c ) if Dk u can be extended to a continuous function on O. C0k+1 (O, K c ) can be considered as a Banach space over K c , with the norm sup |u(t)| + |Dk u(t)| . t∈O Note that coincides with the set of all differentiable Fq -linear functions O → K c . In this section we will obtain a characterization of functions from C01 (O, K c ) Calculus 49 C0k+1 (O, K c ) in terms of coefficients of the expansion u = ∞ cn fn .

Download PDF sample

Analysis in Positive Characteristic by Anatoly N. Kochubei


by Edward
4.4

Rated 4.86 of 5 – based on 26 votes