Hooshmand derived another uniqueness theorem for it which states:
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Later he worked on uniqueness theorems for elliptic and parabolic Phragm�n Lindel�f type theorems.
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By the uniqueness theorem for Fourier expansions, we must then equate the Fourier coefficients term by term, giving
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In mathematical physics, he proved the fundamental uniqueness theorems for the heat equation and studied Volterra integral equations.
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With a suitably enhanced notion of satellite operation called splicing, the JSJ decomposition gives a proper uniqueness theorem for satellite knots.
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See here for a proof of this uniqueness theorem .-talk ) 16 : 44, 15 February 2016 ( UTC)
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The proof of uniqueness for Thompson's sporadic group relied on a smaller uniqueness theorem that was false, so a correction had to be written.
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Note that uniqueness theorems like the Lipschitz one above do not apply to DAE systems, which may have multiple solutions stemming from their ( non-linear ) algebraic part alone.
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The uniqueness theorem for analytic functions also extends to sheaves of analytic functions : if the sheaf of an analytic function contains the zero germ ( i . e ., the sheaf is uniformly zero in some neighborhood ) then the entire sheaf is zero.
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The boundary surfaces may also include boundaries at infinity ( describing unbounded domains )-for these the uniqueness theorem holds if the surface integral vanishes, which is the case ( for example ) when at large distances the integrand decays faster than the surface area grows.
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