![13 State the closed graph theorem and use it to prove the following. Let H be a closed subspace of C[0, 1] which is also clos](http://img.homeworklib.com/images/fe8aad5b-9495-46d2-8c80-8223dffb73bc.png?x-oss-process=image/resize,w_560)
Homework Answers
Add Answer to:
13 State the closed graph theorem and use it to prove the following. Let H be a closed subspace o...
Problem 3. Read about compactness in Section 2.8 of the book. Then, prove, WITHOUT RELYING ON HEINE-BOREL's THEOREM, the following. Let E be a closed bounded subset of E and r be any function...
Problem 3. Read about compactness in Section 2.8 of the book. Then, prove, WITHOUT RELYING ON HEINE-BOREL's THEOREM, the following. Let E be a closed bounded subset of E and r be any function mapping E to (0,00). Then there ensts finitely many pints yi E E,i = 1, , N such that i-1 Here Br(y.)(y) is the open ball (neighborhood) of Tudius r(y.) centered at yi.
Problem 3. Read about compactness in Section 2.8 of the book. Then, prove,...
Topology (c) Let P denote the vector subspace of C1O, 1] consisting of polynomial functions on [0,1. Let P be the closure of P in the sup norm of C[o, 1]. (i) Show that 5 is closed under pointwise mu...
Topology
(c) Let P denote the vector subspace of C1O, 1] consisting of polynomial functions on [0,1. Let P be the closure of P in the sup norm of C[o, 1]. (i) Show that 5 is closed under pointwise multiplication, that is,if f,0€万 then fg P and, moreover, llfglloo for all f,g E P
(c) Let P denote the vector subspace of C1O, 1] consisting of polynomial functions on [0,1. Let P be the closure of P in the sup...
Let A e Cpxp,A e C, and let 11-11 a multiplicative norm on Cpxp. Use Theorem 7.27 of your lecture notes to show that if Al > ll All , then 1. XIp A is invertible and Ip Theorem 7.27. If Il is a su...
Let A e Cpxp,A e C, and let 11-11 a multiplicative norm on Cpxp. Use Theorem 7.27 of your lecture notes to show that if Al > ll All , then 1. XIp A is invertible and Ip Theorem 7.27. If Il is a sub-multiplicative norm on C, then pl 1. Moreover, i X E CPXP and |X|l < 1, then 1. Ip X is invertible. 2. (1,-X)-1-).X' ; i.e., the sum converges j-0 SI
Let A e Cpxp,A e...
10. Prove the following theorem Theorem 1 Let H and H denote the input-output transfer functions for the continuous tim...
10. Prove the following theorem Theorem 1 Let H and H denote the input-output transfer functions for the continuous time systems associated with state matrices (A, B, C) and (A, B,C), respectively. Thus the systems have state representations (t) = Ar(t)+Bu(t) t)C(t) 1(t y(t) and Ci(t) = Assume system (A B. C) and (A. B,C) are equivalent representations, and hence there erists an invertible matriz P such that i(t) = Pa (t) defines a coordinate transformation between the two systems...
Real Analysis II Please do it without using Heine-Borel's theorem and do it only if you're sure Problem: Let E be a closed bounded subset of En and r be any function mapping E to (0,∞). Then t...
Real Analysis II
Please do it without using Heine-Borel's theorem
and do it only if you're sure
Problem: Let E be a closed bounded subset of
En and r be any function mapping E to
(0,∞). Then there exists finitely many points yi ∈ E, i
= 1,...,N such that
Here Br(yi)(yi) is the open ball
(neighborhood) of radius r(yi) centered at
yi.
Also, following definitions & theorems should help
that
E CUBy Definition. A subset S of a topological...
#23 22, Use the definition of limit to prove Theorem 3.5. 23. Use Theorem 3.5 to...
#23
22, Use the definition of limit to prove Theorem 3.5. 23. Use Theorem 3.5 to prove that lim x? cost(1/x)-0. In addition, give a proof of th result without using Theorem 3.5. THEOREM 3.5 Squeeze Theorem for Functions Let I be an open interval that contains the point c and suppose that f, g, except possibly at the point c. Suppose that g(x) s f(a) s h(x) for all x in I If limn g(x)-L = lim h (x),...
(a) Let S be the area of a bounded and closed region D with boundary дD of a smooth and simple cl...
(a) Let S be the area of a bounded and closed region D with boundary дD of a smooth and simple closed curve, show that S Jlxy -ydx by Green's Theorem. (Hint: Let P--yandQ x) (b) Let D = {(x,y) 1} be an ellipse, compute the area of D a2 b2 (c) Let L be the upper half from point A(a, 0) to point B(-a, 0) along the elliptical boundary, compute line integral I(e* siny - my)dx + (e* cos...
This is a tough **Real Analysis** problem, please do it without Heine Borel's theorem & provide as much details as possible Let E be a closed bounded subset of E" and r be any function...
This is a tough **Real Analysis** problem, please do
it without Heine Borel's theorem & provide as much details as
possible
Let E be a closed bounded subset of E" and r be any function mapping E to (0,00). Then there exists finitely many pints yi E E, i = 1, . .. ,N such that ECUBvi) Here Bry(yi) is the open ball (neighborhood) of radius r(y) centered at y
Let E be a closed bounded subset of E" and...
·J (I) < 0 for all such y. (Hint: let g(x)--f(x) and use part (a)) 3....
·J (I) < 0 for all such y. (Hint: let g(x)--f(x) and use part (a)) 3. In this problem, we prove the Intermedinte Value Theorem. Let Intermediate Value Theorem. Let f : [a → R be continuous, and suppose f(a) < 0 and f(b) >0. Define S = {t E [a, b] : f(z) < 0 for allェE [a,t)) (a) Prove that s is nonempty and bounded above. Deduce that c= sup S exists, and that astst (b) Use Problem...
1. (a) State and prove the Mean-Value Theorem. You may use Rolle's Theorem provided you state...
1. (a) State and prove the Mean-Value Theorem. You may use Rolle's Theorem provided you state it clearly (b) A fired point of a function g: (a, bR is a point cE (a, b) such that g(c)-c Suppose g (a, b is differentiable and g'(x)< 1 for all x E (a, b Prove that g cannot have more than one fixed point. <「 for (c) Prove, for all 0 < x < 2π, that sin(x) < x.
Problem 3. Read about compactness in Section 2.8 of the book. Then, prove, WITHOUT RELYING ON HEINE-BOREL's THEOREM, the following. Let E be a closed bounded subset of E and r be any function mapping E to (0,00). Then there ensts finitely many pints yi E E,i = 1, , N such that i-1 Here Br(y.)(y) is the open ball (neighborhood) of Tudius r(y.) centered at yi.
Problem 3. Read about compactness in Section 2.8 of the book. Then, prove,...
Topology
(c) Let P denote the vector subspace of C1O, 1] consisting of polynomial functions on [0,1. Let P be the closure of P in the sup norm of C[o, 1]. (i) Show that 5 is closed under pointwise multiplication, that is,if f,0€万 then fg P and, moreover, llfglloo for all f,g E P
(c) Let P denote the vector subspace of C1O, 1] consisting of polynomial functions on [0,1. Let P be the closure of P in the sup...
Let A e Cpxp,A e C, and let 11-11 a multiplicative norm on Cpxp. Use Theorem 7.27 of your lecture notes to show that if Al > ll All , then 1. XIp A is invertible and Ip Theorem 7.27. If Il is a sub-multiplicative norm on C, then pl 1. Moreover, i X E CPXP and |X|l < 1, then 1. Ip X is invertible. 2. (1,-X)-1-).X' ; i.e., the sum converges j-0 SI
Let A e Cpxp,A e...
10. Prove the following theorem Theorem 1 Let H and H denote the input-output transfer functions for the continuous time systems associated with state matrices (A, B, C) and (A, B,C), respectively. Thus the systems have state representations (t) = Ar(t)+Bu(t) t)C(t) 1(t y(t) and Ci(t) = Assume system (A B. C) and (A. B,C) are equivalent representations, and hence there erists an invertible matriz P such that i(t) = Pa (t) defines a coordinate transformation between the two systems...
Real Analysis II
Please do it without using Heine-Borel's theorem
and do it only if you're sure
Problem: Let E be a closed bounded subset of
En and r be any function mapping E to
(0,∞). Then there exists finitely many points yi ∈ E, i
= 1,...,N such that
Here Br(yi)(yi) is the open ball
(neighborhood) of radius r(yi) centered at
yi.
Also, following definitions & theorems should help
that
E CUBy Definition. A subset S of a topological...
#23
22, Use the definition of limit to prove Theorem 3.5. 23. Use Theorem 3.5 to prove that lim x? cost(1/x)-0. In addition, give a proof of th result without using Theorem 3.5. THEOREM 3.5 Squeeze Theorem for Functions Let I be an open interval that contains the point c and suppose that f, g, except possibly at the point c. Suppose that g(x) s f(a) s h(x) for all x in I If limn g(x)-L = lim h (x),...
(a) Let S be the area of a bounded and closed region D with boundary дD of a smooth and simple closed curve, show that S Jlxy -ydx by Green's Theorem. (Hint: Let P--yandQ x) (b) Let D = {(x,y) 1} be an ellipse, compute the area of D a2 b2 (c) Let L be the upper half from point A(a, 0) to point B(-a, 0) along the elliptical boundary, compute line integral I(e* siny - my)dx + (e* cos...
This is a tough **Real Analysis** problem, please do
it without Heine Borel's theorem & provide as much details as
possible
Let E be a closed bounded subset of E" and r be any function mapping E to (0,00). Then there exists finitely many pints yi E E, i = 1, . .. ,N such that ECUBvi) Here Bry(yi) is the open ball (neighborhood) of radius r(y) centered at y
Let E be a closed bounded subset of E" and...
·J (I) < 0 for all such y. (Hint: let g(x)--f(x) and use part (a)) 3. In this problem, we prove the Intermedinte Value Theorem. Let Intermediate Value Theorem. Let f : [a → R be continuous, and suppose f(a) < 0 and f(b) >0. Define S = {t E [a, b] : f(z) < 0 for allェE [a,t)) (a) Prove that s is nonempty and bounded above. Deduce that c= sup S exists, and that astst (b) Use Problem...
1. (a) State and prove the Mean-Value Theorem. You may use Rolle's Theorem provided you state it clearly (b) A fired point of a function g: (a, bR is a point cE (a, b) such that g(c)-c Suppose g (a, b is differentiable and g'(x)< 1 for all x E (a, b Prove that g cannot have more than one fixed point. <「 for (c) Prove, for all 0 < x < 2π, that sin(x) < x.
Most questions answered within 3 hours.
-
At the start of a CD it is spinning at a rate of 525 rpm
(revolutions...
asked 22 minutes ago -
4. Without doing any calculations, predict whether the observed
∆T would increase, decrease or remain the...
asked 1 hour ago -
Based on the range, which of the following sets of scores has
the greatest variability? 3,...
asked 2 hours ago -
Ripples in a pond travel at a velocity of 3 m/s with one peak
passing a...
asked 2 hours ago -
A man stands on the roof of a building of height 13.0 mm and
throws a...
asked 2 hours ago -
The extent to which assets are financed by borrowed funds and
other liabilities is indicated by:...
asked 3 hours ago -
Explain in detail
Germany is the fifth largest economy
explain what goods and services Germany specializes...
asked 3 hours ago -
The density of platinum is 21.45 g/mL. If a cube of platinum
with a mass of...
asked 4 hours ago -
Accounts Receivable
Sales
A/R Posting
Extended Sales Invoice
Packing Slip
Compare invoice to packing slip 2...
asked 4 hours ago -
Michaella, age 23, is a full-time law student and is claimed by
her parents as a...
asked 4 hours ago -
Why are polymers not typically casted into products?
asked 4 hours ago -
When rolling a die 129 times, what is the probability of rolling
a 6 no more...
asked 4 hours ago