maximum modulus principle वाक्य
उदाहरण वाक्य
मोबाइल
- However, the maximum modulus principle cannot be applied to an unbounded region of the complex plane.
- The maximum modulus principle can therefore be applied to " F " " n " in the strip.
- There is no need for the Borel Carath�odory theorem, but you do need to consider the directions and the Maximum modulus principle.
- 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.
- 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.
- 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.
- 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 }.
- :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)
- 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.
- 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.
- 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.
- If the growth rate of | g | is guaranteed to not be " too fast, " as specified by an appropriate growth condition, the " Phragm�n Lindel�f 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.
- 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.
- 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.
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