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In mathematics, a tube domain is a generalization of the notion of a vertical strip in the complex plane to several complex variables. A strip can be thought of as the collection of complex numbers whose real part lie in a given subset of the real line and whose imaginary part is unconstrained; likewise, a tube is the set of complex vectors whose real part is in some given collection of real vectors, and whose imaginary part is unconstrained.

### Definition

### Tubes as domains of holomorphy

### Hardy spaces