Question #17973
True or False with explanation:-
1.The mean value theorem of a real-valued function of a real variable does not hold in general for complex-valued functions.
2.A real-valued function u in domain D cannot be analytic in D unless it is a constant function.
3.There exists a non-constant real-valued function u in open set D which is analytic in D.
4.A real-valued function u(x,y) is harmonic in D iff u(x,-y) is harmonic in D.
5.If f:D→D’ is analytic and u: D'→R is harmonic then the composition of u & f is harmonic inD.
6.{fn(z)} be a sequence of analytic function in a domain D such that fn→f uniformly inD. Then fn’→f' uniformly in D .
1.The mean value theorem of a real-valued function of a real variable does not hold in general for complex-valued functions.
2.A real-valued function u in domain D cannot be analytic in D unless it is a constant function.
3.There exists a non-constant real-valued function u in open set D which is analytic in D.
4.A real-valued function u(x,y) is harmonic in D iff u(x,-y) is harmonic in D.
5.If f:D→D’ is analytic and u: D'→R is harmonic then the composition of u & f is harmonic inD.
6.{fn(z)} be a sequence of analytic function in a domain D such that fn→f uniformly inD. Then fn’→f' uniformly in D .
Expert's answer
Unfortunately, your question requires a lot of work and cannot be done for free.
Submit it with all requirements as an assignment to our control panel and we'll assist you.
Submit it with all requirements as an assignment to our control panel and we'll assist you.
Learn more about our help with Assignments: Complex Analysis
Comments