Multiplier (Fourier analysis)

About: Multiplier (Fourier analysis) is a research topic. Over the lifetime, 3448 publications have been published within this topic receiving 51845 citations. The topic is also known as: multiplier operator & symbol.

Fourier Integral Operators. I

Abstract: Pseudo-differential operators have been developed as a tool for the study of elliptic differential equations. Suitably extended versions are also applicable to hypoelliptic equations, but their value is rather limited in genuinely non-elliptic problems. In this paper we shall therefore discuss some more general classes of operators which are adapted to such applications. For these operators we shall develop a calculus which is almost as smooth as that of pseudo-differential operators. It also seems that one gains some more insight into the theory of pseudo-differential operators by considering them from the point of view of the wider classes of operators to be discussed here so we shall take the opportunity to include a short exposition.

Multiplier and gradient methods

Abstract: The main purpose of this paper is to suggest a method for finding the minimum of a functionf(x) subject to the constraintg(x)=0. The method consists of replacingf byF=f+λg+1/2cg 2, wherec is a suitably large constant, and computing the appropriate value of the Lagrange multiplier. Only the simplest algorithm is presented. The remaining part of the paper is devoted to a survey of known methods for finding unconstrained minima, with special emphasis on the various gradient techniques that are available. This includes Newton's method and the method of conjugate gradients.

Extremum Problems with Inequalities as Subsidiary Conditions

Abstract: This paper deals with an extension of Lagrange’s multiplier rule to the case, where the subsidiary conditions are inequalities instead of equations Only extrema of differentiable functions of a finite number of variables will be considered There may however be an infinite number of inequalities prescribed Lagrange’s rule for the situation considered here differs from the ordinary one, in that the multipliers may always be assumed to be positive This makes it possible to obtain sufficient conditions for the occurence or a minimum in terms of the first derivatives only

Fourier Integrals in Classical Analysis

Abstract: Background 1. Stationary phase 2. Non-homogeneous oscillatory integral operators 3. Pseudo-differential operators 4. The half-wave operator and functions of pseudo-differential operators 5. Lp estimates of eigenfunctions 6. Fourier integral operators 7. Local smoothing of Fourier integral operators Appendix. Lagrangian subspaces of T*IRn.