Abstract
Let Ω be a domain of the (n + 1)-dimensional space ℝn +1 and φ(x, t) a function continuous in Ω. The closure in Ω of the set of all points (x, t) for which φ(x, t) ≠ 0 is called the support of the function φ(x,t) in Ω and denoted by supp φ(х, t). For an integer q ≥ 0 we denote by C q (Ω) [resp., C q \((\bar{\Omega })\)] the set of all functions φ(х,t) continuous in Ω [resp., \((\bar{\Omega })\)] together with their derivatives of order less than or equal to q. C q0 (Ω) [resp., C ∞0 (Ω)] will designate the set of functions φ(x, t) ∈ C q (Ω) [resp., C ∞(Ω)] with supports in Ω.
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© 1998 Springer Basel AG
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Eidelman, S.D., Zhitarashu, N.V. (1998). Functional Spaces. In: Parabolic Boundary Value Problems. Operator Theory Advances and Applications, vol 101. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8767-0_2
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DOI: https://doi.org/10.1007/978-3-0348-8767-0_2
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9765-5
Online ISBN: 978-3-0348-8767-0
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