A superposition theorem for unbounded continuous functions
A superposition theorem for unbounded continuous functions
Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper R Superscript n"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>R</mml:mi> <mml:mi>n</mml:mi> </mml:msup> </mml:mrow> <mml:annotation encoding="application/x-tex">{R^n}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be the <italic>n</italic>-dimensional Euclidean space. We prove that there are 4<italic>n</italic> real functions <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="phi Subscript q"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>φ<!-- φ --></mml:mi> <mml:mi>q</mml:mi> …