Sentence examples for number of eigenvalues in each from inspiring English sources

Moreover, we are able to count the number of eigenvalues in each cluster.

We obtain bounds on the total number of eigenvalues in the case where V decays exponentially at infinity.

If operator is not semi-bounded we consider the number of eigenvalues in the interval ((0,lambda )) (or ((-lambda,0))) which could be reduced to the asymptotics of the number of eigenvalues in the interval ((-1,0)) (or (0, 1)) of H x, hD, h).

It is observed that the three groups of eigenvalues are overlapped completely since iteration 2, and the number of eigenvalues in any of the three groups is nearly equivalent to that of the real CCM.

As the figures show, even this very little reduction in the energy of the system results in the elimination of a large number of eigenvalues in the SVD scheme.

The resulting hierarchy is then illustrated in a tabular form where the number of eigenvalues for each of the problems is also given.

(i) We are interested in ({mathsf {N}}(0,lambda )), the number of eigenvalues of A in ([0,lambda )).

This work is concerned with obtaining bounds on the number of eigenvalues of L in subsets of the complement of the essential spectrum of L0, in terms of the approximation numbers of the perturbing operator K. Our results can be considered as wide generalizations of classical results on the distribution of eigenvalues of compact operators, which correspond to the case L0="0.

Example 4.2 In this example we evaluate the number of eigenvalues of problem (4.1) in Example 4.1 using the representation of the relative oscillation numbers in the form of (3.30).

We are interested in ({mathsf {N}}(0,lambda )), the number of eigenvalues of (VA^{-1}_B) in ((lambda ^{-1},infty )).

Here, begin{aligned} varkappa _0 = (2pi )^{-d} iint mathbf {n} x,xi ),dx dxi end{aligned} (3.3) where (mathbf {n} x,xi )) is the number of eigenvalues of (A^0 x,xi )) in (0, 1) and (m=m_A) is the order of A. Suppose that (A_B) is positive definite (then (m_Age 2)) and V is an operator of the order (m_B