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2001
The Fourier inversion formula is a standard fact of elementary analysis. Harish-Chandra developed an inversion for K-bi-invariant functions on a semisimple Lie group G, in other words he developed the theory of a spherical transform [Har 58a], [Har 58b], which is an integral transform, with a kernel called the spherical kernel.
Jay Jorgenson, Serge Lang
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The Fourier inversion formula is a standard fact of elementary analysis. Harish-Chandra developed an inversion for K-bi-invariant functions on a semisimple Lie group G, in other words he developed the theory of a spherical transform [Har 58a], [Har 58b], which is an integral transform, with a kernel called the spherical kernel.
Jay Jorgenson, Serge Lang
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Generalized inverses and generalized splines
Numerical Functional Analysis and Optimization, 1980An abstract framework in Hilbert space is provided for generalized splines and generalized inverses of operators.
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2011
Let A be a square matrix of order n. If it is nonsingular, then Ker(A) = {0} and, as mentioned earlier, the solution vector x in the equation y = Ax is determined uniquely as x = A -1 y. Here, A -1 is called the inverse (matrix) of A defining the inverse transformation from y ∈ En to x ∈ Em, whereas the matrix A represents a transformation from x to y.
Haruo Yanai, Kei Takeuchi, Yoshio Takane
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Let A be a square matrix of order n. If it is nonsingular, then Ker(A) = {0} and, as mentioned earlier, the solution vector x in the equation y = Ax is determined uniquely as x = A -1 y. Here, A -1 is called the inverse (matrix) of A defining the inverse transformation from y ∈ En to x ∈ Em, whereas the matrix A represents a transformation from x to y.
Haruo Yanai, Kei Takeuchi, Yoshio Takane
openaire +1 more source