maximum modulus principle造句

例句与造句

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閛dory 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. It's difficult to find maximum modulus principle in a sentence. 用maximum modulus principle造句挺难的
7. He is known for the Picard Lindel鰂 theorem on differential equations and the Phragm閚 Lindel鰂 principle, one of several refinements of the maximum modulus principle that he proved in complex function theory.
8. 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 }.
9. :I'll close my eyes and point to Maximum modulus principle and Borel Carath閛dory theorem ( and then to sci . math when you find I wasn't helpful . ) iames 19 : 22, 13 June 2007 ( UTC)
10. 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.
11. In a typical Phragm閚 Lindel鰂 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.
12. Then we can find a chart from a neighborhood of p _ 0 to the unit disk \ mathbb { D } such that f ( \ phi ^ {-1 } ( z ) ) is holomorphic on the unit disk and has a maximum at \ phi ( p _ 0 ) \ in \ mathbb { D }, so it is constant, by the maximum modulus principle.
13. If the growth rate of | g | is guaranteed to not be " too fast, " as specified by an appropriate growth condition, the " Phragm閚 Lindel鰂 principle " can be applied to show that boundedness of | g | on the region's boundary implies that | g | is in fact bounded in the whole region, effectively extending the maximum modulus principle to unbounded regions.
14. This is known as the " maximum modulus principle . " ( In fact, since \ overline { \ Omega } is compact and | f | is continuous, there actually exists some w _ 0 \ in \ partial \ Omega such that | f ( w _ 0 ) | = \ sup _ { z \ in \ partial \ Omega } | f ( z ) | . ) The maximum modulus principle is generally used to conclude that a holomorphic function is bounded in a region after showing that it is bounded on the boundary of that region.
15. This is known as the " maximum modulus principle . " ( In fact, since \ overline { \ Omega } is compact and | f | is continuous, there actually exists some w _ 0 \ in \ partial \ Omega such that | f ( w _ 0 ) | = \ sup _ { z \ in \ partial \ Omega } | f ( z ) | . ) The maximum modulus principle is generally used to conclude that a holomorphic function is bounded in a region after showing that it is bounded on the boundary of that region.