square integrable function造句

• In the " Schr鰀inger model ", the Heisenberg group acts on the space of square integrable functions.
• The theorem now holds for square integrable functions on G instead of class functions and the subgroup H must be closed.
• This unitary extension of the Fourier transform is what we mean by the Fourier transform on the space of square integrable functions.
• Indeed, there exists a unique series representation for a square integrable function " f " expressed in this basis:
• The Hilbert space may be taken to be the set of square integrable functions on the real number line ( the plane waves ).
• This may be done, by proving, that there exists no non-zero square integrable function on G orthogonal to all the irreducible characters.
• A vector, which represents a state of the system, in the Hilbert space of square integrable functions is represented by | \ Psi _ E \ rangle.
• This distinction is best kept, even if one could argue that two such function spaces are mathematically equal, e . g . being the set of square integrable functions.
• Conversely, if can be decomposed as the product of two square integrable functions and, then the Fourier transform of is given by the convolution of the respective Fourier transforms and.
• The eigenfunctions of the Laplace Beltrami operator on the manifold serve as the embedding dimensions, since under mild conditions this operator has a countable spectrum that is a basis for square integrable functions on the manifold ( compare to Fourier series on the unit circle manifold ).
• To study this equation, consider the space X = L ^ 2 ( a, b ), that is, the Lp space of all square integrable functions u : [ a, b ] \ to \ mathbb R in respect to the Lebesgue measure.
• Let V _ I denote the Hilbert space of all measurable, square integrable functions \ Phi : G \ to V _ \ eta with the property \ Phi ( ls ) = \ eta ( l ) \ Phi ( s ) for all l \ in H, s \ in G . The norm is given by
• Let the Hilbert space V be the Sobolev space H ^ 1 _ 0 ( a, b ), which is the space of all square integrable functions v defined on [ a, b ] that have a weak derivative on [ a, b ] with v'also being square integrable, and v satisfies the conditions v ( a ) = v ( b ) = 0.