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Approximation by Polynomials with Integral Coefficients by Le Baron O. Ferguson is a nonfiction available to read on EtoBox.
What is Approximation by Polynomials with Integral Coefficients about?
Results in the approximation of functions by polynomials with coefficients which are integers have been appearing since that of Pal in 1914. The body of results has grown to an extent which seems to justify this book. The intention here is to make these results as accessible as possible. The book addresses essentially two questions. The first is the question of what functions can be approximated by polynomials whose coefficients are integers and the second question is how well are they approximated (Jackson type theorems). For example, a continuous function $f$ on the interval $-1,1$ can be uniformly approximated by polynomials with integral coefficients if and only if it takes on integral values at $-1,0$ and $+1$ and the quantity $f(1)+f(0)$ is divisible by $2$. The results regarding the second question are very similar to the corresponding results regarding approximation by polynomials with arbitrary coefficients. In particular, nonuniform estimates in terms of the modules of continuity of the approximated function are obtained. Aside from the intrinsic interest to the pure mathematician, there is the likelihood of important applications to other areas of mathematics; for exampl
Who reads Approximation by Polynomials with Integral Coefficients?
It is typically read by self-directed learners exploring a subject in depth.
Common subject areas: history, science, philosophy, social sciences.
- Author
- Le Baron O. Ferguson
- Publisher
- American Mathematical Society
- Published
- 1980
- Language
- EN
- ISBN
- 9780821815175
- Category
- nonfiction
- Subjects
- Mathematics, Stem