Herfort, Hofmann, and Russo deal with periodic locally compact groups, specifying that a locally compact group is periodic if there are no non-singleton connected
subspaces in it, and if every element in it is contained in a compact subgroup.
Next, we define for equation (1) the sequence of
subspaces [H.sub.k] of [epsilon] by the recursive formula
Widely used methods for the solution of this type of problem include methods based on Krylov
subspaces, i.e., of Arnoldi and Lanczos type, e.g., [1, 14, 23].
are the projection matrices of the signal and noise
subspaces extracted from subarray i, i = 1,2, respectively, and [[??].sup.(1)] is a rough DOA estimation result reduced by using root-MUSIC with the extracted noise projection matrix [P.sub.n] given by (28).
For the case of free locally convex spaces on compact metrizable spaces Y, our Theorem 8 gives a complete description of those
subspaces X of Y with the property that L(X) can be embedded as a topological vector
subspace of L(Y).
Furthermore, authors have shown that CLBS is closely related to the invariant
subspace; namely, exact solutions defined on invariant
subspaces for equations or their variant forms can be obtained by using the CLBS method [12-24].
For k [member of] N, consider a sequence of Krein space contractions [A.sub.k] : [H.sub.k] [right arrow] [K.sub.k], where [H.sub.k] and [K.sub.k] are nested regular
subspaces of some Krein spaces U and Y, respectively.
For this purpose, we evenly divide the RGB space into the eight
subspaces {v_black, v_red, v_green, v_blue, v_yellow, v_pink, v_cyan, v_white}, which are defined by the well-defined colors: {black, red, green, blue, yellow, pink, cyan, white}, at their corresponding vertices of the RGB space, as shown in Figure 1(a).