# A Treatise on Trigonometric Series. Volume 1 - download pdf or read online

By N. K. Bary

ISBN-10: 1483199169

ISBN-13: 9781483199160

**Read or Download A Treatise on Trigonometric Series. Volume 1 PDF**

**Best mathematics_1 books**

- Axiomatics of classical statistical mechanics
- An Introduction to Hydrodynamics and Water Waves
- Numerical Mathematics and Applications
- Men of Mathematics: The Lives and Achievements of the Great Mathematicians from Zeno to Poincare

**Extra resources for A Treatise on Trigonometric Series. Volume 1**

**Example text**

20. Linear functionals in Lp(p > 1) Let f(pc)eLp [a, b], p > 1. 1) then U(f) is a linear functional in LP [a,b]. 1) holds. We have THEOREM. Ifq is defined by the equation 1 1 - + - = 1, p q then any linear functional in LP [a, b] has the form b U(J) = j f(x)g(x)dx, q a where g(x) eL [a,b], (See Lyusternik and Sobolev, réf. A18, p. 170). 2). This last statement is proved very easily. 4) if||/llLP

It is orthogonal over any interval of length 2π (see § 5). , if the system fos-·"} *■-ft ±'·■·■)· is considered, then it is also normal. § 10. f DEFINITION. The system of functions {

The class of functions {/(*)} belonging to LP forms an everywhere dense set in LP, p > 1, if for any e > 0 and for any yeLP a function / c a n be found such that U-

### A Treatise on Trigonometric Series. Volume 1 by N. K. Bary

by Kenneth

4.3