Prove that there is no continuous function whose Fourier coefficients satisfy |ak(f)| > 1/k for k

Question:

Prove that there is no continuous function whose Fourier coefficients satisfy |ak(f)| > 1/√k for k ∈ N.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

An Introduction to Analysis

ISBN: 978-0132296380

4th edition

Authors: William R. Wade

See More Books

Question Posted: Mar 29, 2016 04:29 AM

See More Questions

Let B denote the closed unit ball in a finite-dimensional normed linear space B = {x X: ||x|| 1} and let S denote its boundary, that is, S = {x X: ||x|| 1} There is no continuous function r: B S...
Explain in detail why there is no continuous function y(x) such that the inner product identity (11.39) holds for every continuous function u(x).
Prove that there is no positive integer n such that n2 + n3 = 100.
inary Differential Equations > Assessment 10.1-10.2 Score: 0.25/3 1/3 answered "X" Question 2 < Submit Question > Gradebook Convert the differential equation `u" -3 u' -4 u = e^(-t)` into a system of...
Use a tax service, such as United States Tax Reporter, to answer the following questions: a. If your school provides an athletic scholarship to an athlete, does the athlete have gross income? b. Can...
The active ingredient of aspirin tablets is acetylsalicylic acid, which has a density of 1.4 g/cm 3 . In a lab class, a student used paper chromatography to isolate another common ingredient of...
1 What factors such as the history or current context of the company appear to influence the way the company handles these financial and budgeting processes? Does the current approach appear to be...
Gilbert Moss and Angela Pasaic spent several summers during their college years working at archaeological sites in the Southwest. While at those digs, they learned how to make ceramic tiles from...
8. A bank has offered you a $500,000 mortgage at a quoted rate of 4%. The mortgage calls for monthly payments based on a 20-year amortization period. What discount rate would you use to find the...
The inductor of figure has the following dimensions: a = h = w = 1.5cm b = 2cm g = 0.2cm The winding factor (i.e., the fraction of the total winding area occupied by conductor) is fw = 0.55. The...
If f is integrable on [-Ï, -] and a R, prove that linLf(x)sin(k+)xdx=0.
Prove that if f: R R belongs to C2(R) and f, f' are both periodic, then Sf converges to f uniformly and absolutely on R. (See also Exercise 14.4.5.)
You have a 200- resistor, a 0.400-H inductor, and a 6.00-F capacitor. Suppose you take the resistor and inductor and make a series circuit with a voltage source that has voltage amplitude 30.0 V and...
The break even point of a company is $240 000. They sell their product at a markup of 30% and have variable expenses of 9% of sales. They currently make a profit of $10 500. They plan on reducing...
What kind of messages are young girls and boys receiving about whether their safety in relationships is valued are by their families and communities? Do we emphasize to our children (boys and girls)...
Below are the transactions for Oliver Printing, Incorporated for June, the first month of operations. June 1 Obtain a loan of $ 5 6 , 0 0 0 from the bank by signing a note. June 2 Issue common stock...
Assume an organization must invest $ 7 0 0 , 0 0 0 in fixed costs to produce a product that sells for $ 7 5 and requires $ 4 0 in variable costs to produce one unit. What is the organization s...
hotel delta marriott montreal What do you think is the value and purpose for the hotel brand choosing to make CSR an important part of their overall business strategy? What two recommendations based...
Ive brought shame on myself, my family and the profession were the words of Tim Donaghy, as a federal district judge sentenced him to 15 months behind bars in July 2008. Formally, the charges against...
Q1) What is the a3 Value Q2) What is the a7 Value Q3) What is the a4 Value Q4) What is the b3 Value Q5) What is the b2 Value Q6) What is the sign of 2nd constraint? A pastry chef at a bakery wants to...
Shown is the graph of the population function P(t) for yeast cells in a laboratory culture. Use the method of Example 1 to graph the derivative P'(t). What does the graph of P' tell us about the...
The graph shows how the average age of first marriage of Japanese men varied in the last half of the 20th century. Sketch the graph of the derivative function M'(t). During which years was the...
Make a careful sketch of the graph of f and below it sketch the graph of f in the same manner as in Exercises 513. Can you guess a formula for f (x) from its graph? 16. f(x) = sin xr 17. f(x) - e 18....
The Balance Sheet has accounts where the accountant must make estimates. Some situations in which estimates affect amounts reported in the balance sheet include: Allowance for doubtful accounts....
Alado fis istirmerfs Tat likifond 205L [ridont inip lanod whadtinion? hingend is antan Qultit foer avdeed Divdasit errem yodichiders Etexlpoges Getmare nelp
The limitation on the deduction of business interest does not apply to non-corporate taxpayers. course hero True or False explain?

Prove that there is no continuous function whose Fourier coefficients satisfy |ak(f)| > 1/k for k

Question:

Step by Step Answer:

If f were continuo...View the full answer

An Introduction to Analysis

Students also viewed these Numerical Analysis questions