Let R a, b Atilde c, d be a rectangle in R2 A function f is said to have separated variables if for some scalars ck and functions fk C a, b , gk C c, d Prove that given f C(R) there is a sequence of functions with separated variables, Pn, such that Pn f uniformly on R as n CA ft(x)gx(y) P(x, y) C f...

Since collection of functions with separated variables i ...

Let R = [a, b] Ã [c, d] be a rectangle in R2. A function f is

Question:

Let R = [a, b] Ã— [c, d] be a rectangle in R2. A function f is said to have separated variables if

for some scalars ck and functions fk ˆˆ C[a, b], gk ˆˆ C[c, d]. Prove that given f ˆˆ C(R) there is a sequence of functions with separated variables, Pn, such that Pn †’ f uniformly on R as n †’ ˆž.

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 04:18 AM

See More Questions

Use Exercise 10.7.3 to prove that if f C([a, b] Ã [c, d]), then f(x, y)dy dx- fx.)dx) dy
Let H be a nonempty, closed, bounded subset of Rn. a) Suppose that f : H Rm is continuous. Prove that is finite and there exists an x0 H such that ||f(x0)|| = ||f||H. b) A sequence of functions fk: H...
Let T = [0, 2). a) Prove that the function (x) := (cos x, sin x) is 1-1 from T onto B1(0, 0) R2. b) Prove that p(x, y) := || (x) - (y)|| is a metric on T. c) Prove that a function f is continuous on...
Do firms follow the same steps for impairment testing of finite- and indefinite- life intangible assets ? Explain.
What factors influence a U.S. business firm to go overseas?
In Exercises 15 through 20, approximate the given integral and estimate the error |E n | using (a) The trapezoidal rule (b) Simpsons rule with the specified number of subintervals. J1 In x dx; n = 4
With reference to Exercise 11.39, analyze the residuals from the regression plane. Data From Exercise 11.39 11.39 The following sample data were collected to determine the relationship between...
Roniger Products Company operates three divisions, each with its own manufacturing plant and marketing/sales force. The corporate headquarters and central accounting office are in Roniger, and the...
25 28 30 30 Sheridan Manufacturing Company uses a job order cost system and keeps perpetual inventory records. June 1 Purchased raw materials for $22,800 on account. 8 Raw materials requisitioned by...
A. Richard McCarthy (born 2/14/64; Social Security number 100-10-9090) and Christine McCarthy (born 6/1/1966; Social security number 101-21-3434) have a 19-year-old son (born 10/2/99 Social Security...
A polynomial on Rn is a function of the form where the aj1,. . . . . .. j n 's are scalars and N1,...,Nn N. Prove that if A is compact in Rn and f C(A), then there is a sequence of polynomials Pk on...
Use Exercise 10.7.1 to prove that if f C[a, b] and For k = 0, 1,..., then f(x) = 0 for all x [a, b). Ja f(x) xk dx = 0
Consider the data set given in Exercise 59. Which of the options below do you think is better for representing the data? Explain your reasoning. Option 1: reporting the mean of all of the vehicles...
What would be the Canadian equivalent of an S-Corp?
How does budget control help the restaurants to improve their financial performance? List any three
During which phase of the cell cycle does the DNA duplicate into two identical copies?
In general, when should a gain from an intercompany sale be recognized? Give reference.
Detail the intricate process of oxygen transport, delineating its journey from inhalation within the pulmonary system to its utilization within the mitochondria, encompassing the physiological...
In Exercises decide whether the function has an inverse function. If so, what is the inverse function? h(t) is the height of the tide t hours after midnight, where 0 t < 24.
Refer to the data in QS 10-1. Based on financial considerations alone, should Helix accept this order at the special price? Explain.
Consider the no-intercept model Y = Bx + E with the Es NID (0, 2). The estimate of 2 is s2 = (yi Bxi) 2 / (n 1) and v(B) = 2 / = 1x2/i (a) Devise a test statistic for H0: B = 0 versus H1: B...
The type II error probability for the t-test for H0: B1 = B1, 0 can be computed in a similar manner to the t-tests of Chapter 9. If the true value of B1 is B1, the value =|B1, 0 B1/((n 1)/Sxx is...
Refer to the data in Exercise 11-1 on y = intrinsic permeability of concrete and x = compressive strength. Find a 95% confidence interval on each of the following: (a) Slope (b) Intercept (c) Mean...
What are some scholarly sources that support the implementation of a case manager?
Review your own current processes relating to ER and IR within the organisation and identify three issues that can be improved upon.
A group of students working on a collaborative research project needs a centralized space to store and edit their documents. Which Teams feature should they primarily use?

Let R = [a, b] Ã [c, d] be a rectangle in R2. A function f is

Question:

CA ft(x)gx(y) P(x, y) = C fi C)g«(y) %3D k=1

Step by Step Answer:

Since collection of functions with separated variables i...View the full answer

An Introduction to Analysis

Students also viewed these Numerical Analysis questions