Often, a complex domain serves as the domain of definition for a holomorphic function.
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This is because the position operator is unbounded, and \ psi has to be chosen from its domain of definition.
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The initial impetus was to have a description of the properties of the domain of definition of the ( maximal ) analytic continuation of an analytic function.
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A partial function is said to be injective or surjective when the total function given by the restriction of the partial function to its domain of definition is.
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The natural domains of definition of functions, continued to the limit, are called " Stein manifolds " and their nature was to make sheaf cohomology groups vanish.
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In the n = 1 case, every open set is a domain of holomorphy : we can define a holomorphic function with zeros natural boundary for a domain of definition of its reciprocal.
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However, in some cases, the formulas of do not give a correct principal value, as giving a domain of definition which is too small and, in one case non-connected.
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Assume that this PDE is non-degenerate in the sense that F _ { u _ x } and F _ { u _ y } are not both zero in the domain of definition.
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For specifying the branch, that is defining which value of the multivalued function is considered at each point, one generally define it at a particular point, and deduce the value everywhere in the domain of definition of the principal value by analytic continuation.
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"' Exponential growth "'occurs when the domain of definition with equal intervals, it is also called "'geometric growth "'or "'geometric decay "', the function values forming a geometric progression.
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