Sökning: "power series algebra"
Visar resultat 6 - 10 av 11 avhandlingar innehållade orden power series algebra.
6. Systems of Linear First Order Partial Differential Equations Admitting a Bilinear Multiplication of Solutions
Sammanfattning : The Cauchy–Riemann equations admit a bilinear multiplication of solutions, since the product of two holomorphic functions is again holomorphic. This multiplication plays the role of a nonlinear superposition principle for solutions, allowing for construction of new solutions from already known ones, and it leads to the exceptional property of the Cauchy–Riemann equations that all solutions can locally be built from power series of a single solution z = x + iy ∈ C. LÄS MER
7. A graded subring of an inverse limit of polynomial rings
Sammanfattning : We study the power series ring R= K[[x1,x2,x3,...]]on countably infinitely many variables, over a field K, and two particular K-subalgebras of it: the ring S, which is isomorphic to an inverse limit of the polynomial rings in finitely many variables over K, and the ring R', which is the largest graded subalgebra of R. LÄS MER
8. Integral Closure and Related Operations on Monomial Ideals
Sammanfattning : The motivation for this thesis starts with the theory of Hilbert coefficients. It is a well known fact that given an ideal I the integral closure Ī can be defined as the largest ideal with the same multiplicity as I. For monomial ideals there is an alternative definition. LÄS MER
9. Amoebas, Discriminants, and Hypergeometric Functions
Sammanfattning : This thesis consists of six chapters. In Chapter 1 we give some historical background to the topic of the thesis together with the fundamental definitions and results that the thesis is based on. In Chapter 2 we study Mellin transforms of rational functions and investigate their analytic continuations. LÄS MER
10. On the linearization of non-Archimedean holomorphic functions near an indifferent fixed point
Sammanfattning : We consider the problem of local linearization of power series defined over complete valued fields. The complex field case has been studied since the end of the nineteenth century, and renders a delicate number theoretical problem of small divisors related to diophantine approximation. LÄS MER