4.i) Prove that the seriesΣsin nxn2n=1converges pointwise on R, and uniformly on any finite interval.. Callits sum f(x).ii) Obtain the Fourier series of the function g defined byg(z) = | f(t)dt,justifying your method by referring to appropriate theorems.iii) What can you say about continuity and smoothness of the functiong? Explain.

According to the guidelines, we are required to solve only the first two sub-questions. Kindly post…

4. i) Prove that the series sin nx n2 n=1 converges pointwise on R, and uniformly on any finite interval.. Call its sum f(x). ii) Obtain the Fourier series of the function g defined by g(x) = | f(t)dt, justifying your method by referring to appropriate theorems. iii) What can you say about continuity and smoothness of the function g? Explain.

4. i) Prove that the series sin nx n2 n=1 converges pointwise on R, and uniformly on any finite interval.. Call its sum f(x). ii) Obtain the Fourier series of the function g defined by g(x) = | f(t)dt, justifying your method by referring to appropriate theorems. iii) What can you say about continuity and smoothness of the function g? Explain.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 17EQ

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