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Functional Analysis
(Linear extension) Let Z be a proper subspace of an n-dimensional
vector space X, and let f be a linear fimctional on Z Show that f can
be extended linearly to X, that is, there is a linear functioned f on X
such that f ̃|z =f
vector space X, and let f be a linear fimctional on Z Show that f can
be extended linearly to X, that is, there is a linear functioned f on X
such that f ̃|z =f
Functional Analysis
Funds flow analysis represents a stock to flow linkage.” – Justify
Functional Analysis
If $T\in\mathcal{B}(X,Y)$ is not compact can the restriction of $T$ to an infinite dimensional subspace of $X$ be compact?
Functional Analysis
If $T\in\mathcal{B}(X,Y)$ is not compact can the restriction of $T$ to an infinite dimensional subspace of $X$ be compact?
Functional Analysis
if T belongs to b(X,Y) is not compact can the restriction of T to an infinite dimensional subspace of X be compact?
Functional Analysis
What are the largest and smallest values of 2x + y on the circle x^2 + y^2 = 1? Where do these values occur? What does this have to do with eigenvectors and eigenvalues?
Functional Analysis
Given the constants c and d, please find the largest and smallest values of cx + dy taken over all points (x,y) of the ellipse x^2/a^2 + y^2/b^2 = 1.
Functional Analysis
Find the product (x+y+z)(1/x+1/y+1/z) and deduce that the least value of this product, over non-negative x,y, and z, is 9. Use this to find the least value of the function f(x,y,z) = 1/x+1/y+1/z, over non-negative x,y, and z, having a constant sum C.
Functional Analysis
When will be f(x) = g(y), if f(x) = g(y) does it mean x=y?
Functional Analysis
(a) Find the Fourier sine transform of e^(-x), x>= 0.
(b) Show that the integral from 0 to infinity of (xsinmx)/(x^2+1) dx = (pi/2)e^-m, m>0 by using the result in (a)
(b) Show that the integral from 0 to infinity of (xsinmx)/(x^2+1) dx = (pi/2)e^-m, m>0 by using the result in (a)
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