maximum modulus principle meaning in Hindi

Examples

1. However, the maximum modulus principle cannot be applied to an unbounded region of the complex plane.
2. The maximum modulus principle can therefore be applied to " F " " n " in the strip.
3. There is no need for the Borel Carath�odory theorem, but you do need to consider the directions and the Maximum modulus principle.
4. Alternatively, the maximum modulus principle can be viewed as a special case of the open mapping theorem, which states that a nonconstant holomorphic function maps open sets to open sets.
5. Reshetnyak's theorem implies that all pure topological results about analytic functions ( such that the Maximum Modulus Principle, Rouch?s theorem etc . ) extend to quasiregular maps.
6. He is known for the Picard Lindel�f theorem on differential equations and the Phragm�n Lindel�f principle, one of several refinements of the maximum modulus principle that he proved in complex function theory.
7. Because S _ { x _ 0 } is a bounded region, the maximum modulus principle is applicable and implies that | gh _ \ epsilon | \ leq 1 for all z \ in S _ { x _ 0 }.
8. :I'll close my eyes and point to Maximum modulus principle and Borel Carath�odory theorem ( and then to sci . math when you find I wasn't helpful . ) iames 19 : 22, 13 June 2007 ( UTC)
9. Since the complex semigroup has as Shilov boundary the symplectic group, the fact that this representation has a well-defined contractive extension to the semigroup follows from the maximum modulus principle and the fact that the semigroup operators are closed under adjoints.
10. In a typical Phragm�n Lindel�f argument, we introduce a multiplicative factor h _ \ epsilon to " subdue " the growth of g, such that | gh _ \ epsilon | is bounded on the boundary of a bounded subregion of S and we can apply the maximum modulus principle to gh _ \ epsilon.