where χ is a scalar function (of space and time or of space-time) which can be chosen arbitrarily.
Bochner spaces are often used in a functional analysis approach to the study of partial differential equations that depend on time, e.g., the heat equation: if the temperature g ( t, x ) is a scalar function of time and space, one can write ( f ( t ) ) ( x ) : = g ( t, x ) to make f a function of time, with f ( t ) being a function of space, possibly in some Bochner space.
The second bedroom could double as a den or study, providing a dual function of part-time sleeping space and daily functional space for the parents.
the formulation of the spacing law in function of the spacing parameter in the decision rules table deriving method.
The number of positions C 1 and FSs being obviously the same, we have proposed a formulation of the spacing law in function of the spacing parameter PSG[37, 38].
Denote by the continuous functions space on, by the absolutely continuous functions space on, by the generalized absolutely continuous functions space on, and by the space of -integrable functions from to.
The dimension of the polynomial ring F[x] introduced above is countably infinite, a basis is given by,,, A fortiori, the dimension of more general function spaces, such as the space of functions on some (bounded or unbounded) interval, is infinite.
As is well known, Triebel-Lizorkin spaces are the unification of several classical function spaces such as Lebegue spaces L p ( R d ), Sobolev spaces H p s ( R d ), Lipschitz spaces C s ( R d ), and so on.
The solutions are continuous functions of both space and time.
Our method requires the introduction of two new function spaces: the space BMO of functions with "bounded mean oscillation" and its predual, the atomic Hardy space H1.
Next we give a lemma from Simon [14], which gives the embedding between fractional Sobolev spaces and spaces of continuous functions, for vector spaces on an interval.
