Results 321 to 330 of about 6,138,106 (354)

Compact Linear Operators

1993
In a sense, nonlinear analysis doesn’t require a very long attention span. A few chapters ago, we were concerned with algebraic topology in the theory of the Brouwer degree; the previous chapter gave us a brief but bracing dip into the sea of point-set topology; and in this chapter we will discuss some topics in classical “linear” functional analysis.
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Non-linear factorization of linear operators

Bulletin of the London Mathematical Society, 2009
We show, in particular, that a linear operator between finite-dimensional normed spaces, which factors through a third Banach space Z via Lipschitz maps, factors linearly through the identity from L(infinity)([0, 1], Z) to L(1)([0, 1], Z) (and thus, in particular, through each L(p)(Z), for 1 < p < infinity) with the same factorization constant.
Johnson, W. B., Maurey, Bernard, Schechtman, G.   +2 more
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Bounded Linear Operators

2003
The first section gives several characterizations of bounded linear operators and proves that a symmetric operator whose domain is the whole Hilbert space is actually bounded (Hellinger-Toeplitz theorem). Several concrete examples of bounded linear operators in Hilbert spaces are discussed in the second section. In Section 3 the vector space \(\mathcal{
Erwin Brüning, Philippe Blanchard
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Solutions of Asymptotically Linear Operator Equations via Morse Theory.

, 1981
: In this paper, we use the classical Morse theory of critical points to study the existence and multiplicity of solutions of a class of asymptotically linear operator equations.
Kung-Ching Chang
semanticscholar   +1 more source

Generalized Inverses in Reproducing Kernel Spaces: An Approach to Regularization of Linear Operator Equations

, 1974
In this paper a study of generalized inverses of linear operators in reproducing kernel Hilbert spaces (RKHS) is initiated. Explicit expressions for generalized inverses and minimal-norm solutions of linear operator equations in RKHS are obtained in ...
M. Nashed, G. Wahba
semanticscholar   +1 more source

On the Convergence of the Conjugate Gradient Method for Singular Linear Operator Equations

, 1972
Let $T:X \to Y$ be a bounded linear operator between two Hilbert spaces X and Y, and let $T^\dag $ denote the generalized inverse of T, and $\Re (T)$ the range of T.
W. J. Kammerer, M. Nashed
semanticscholar   +1 more source

Linear Spaces and Linear Operators

1986
The present chapter is concerned with the basic setting for a great deal of modern mathematical analysis and applied mathematics: the linear or vector space. In a linear space, addition, subtraction, magnification and contraction of elements are all possible, and sometimes even multiplication between elements is possible.
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Steepest Descent for Singular Linear Operator Equations

, 1970
Let H be a Hilbert space, T a bounded linear operator on H into H such that the range of T is closed. Let $T^ * $ denote the adjoint of T. In this paper, we establish the convergence of the method of steepest descent to a solution of the equation $T ...
M. Nashed
semanticscholar   +1 more source

The Structure of a Linear Operator

1992
In this chapter, we study the structure of a linear operator on a finite dimensional vector space, using the powerful module decomposition theorems of the previous chapter. Unless otherwise noted, all vector spaces will be assumed to be finite dimensional.
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The linear products and operations

2007
Publisher Summary This chapter presents two ways to implement the linear products and operations of geometric algebra. Both implementation approaches are based on the linearity and distributivity of the products and operations. The first approach uses linear algebra to encode the multiplying element as a square matrix acting on the multiplied element,
Leo Dorst, Daniel Fontijne, Stephen Mann
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