Kurzweil-stieltjes Integral: Theory And ApplicationsWorld Scientific, 26. 9. 2018 - Počet stran: 400 The book is primarily devoted to the Kurzweil-Stieltjes integral and its applications in functional analysis, theory of distributions, generalized elementary functions, as well as various kinds of generalized differential equations, including dynamic equations on time scales. It continues the research that was paved out by some of the previous volumes in the Series in Real Analysis. Moreover, it presents results in a thoroughly updated form and, simultaneously, it is written in a widely understandable way, so that it can be used as a textbook for advanced university or PhD courses covering the theory of integration or differential equations. |
Obsah
1 | |
7 | |
3 Absolutely continuous functions | 57 |
4 Regulated functions | 73 |
5 RiemannStieltjes integral | 89 |
6 KurzweilStieltjes integral | 139 |
7 Generalized linear differential equations | 245 |
8 Miscellaneous additional topics | 291 |
363 | |
377 | |
Symbol index | 381 |
Další vydání - Zobrazit všechny
Kurzweil-Stieltjes Integral: Theory and Applications Milan Tvrdý,Giselle Antunes Monteiro,Antonín Slavík Náhled není k dispozici. - 2018 |
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absolutely convergent arbitrary ɛ Banach space bounded variation Cauchy Cauchy matrix condition Consequently Consider continuous linear functional convergence theorem Corollary countable d-fine partition defined Definition denoted dg(s division dµg Exercise exists and equals exponential function f dg exists f(aj finite step function fn dg fn(x fo f dg fo f(x formula function f functions of bounded g(aj gauge given Hence implies inequality integrable with respect integral fo f interval Krejčí Kurzweil-Stieltjes integral L(Rn Lebesgue integrable Lebesgue-Stieltjes integral left-continuous Lemma Let f matrix Monteiro Moreover nondecreasing nonnegative proof is complete prove real numbers regulated functions Remark respect to g result Riemann integral Riemann-Stieltjes integral S(fn satisfies Schwabik sequence Stieltjes integral subinterval substitution theorem tion Tvrdý uniformly convergent uniformly integrable unique solution V-integrals var(f vara δε µg-measurable