120 research outputs found
Analysis of an Inverse Problem Arising in Photolithography
We consider the inverse problem of determining an optical mask that produces
a desired circuit pattern in photolithography. We set the problem as a shape
design problem in which the unknown is a two-dimensional domain. The
relationship between the target shape and the unknown is modeled through
diffractive optics. We develop a variational formulation that is well-posed and
propose an approximation that can be shown to have convergence properties. The
approximate problem can serve as a foundation to numerical methods.Comment: 28 pages, 1 figur
Interpolation Theorems for Self-adjoint Operators
We prove a complex and a real interpolation theorems on Besov spaces and
Triebel-Lizorkin spaces associated with a selfadjoint operator , without
assuming the gradient estimate for its spectral kernel. The result applies to
the cases where is a uniformly elliptic operator or a Schr\"odinger
operator with electro-magnetic potential.Comment: 8 pages. Submitte
Comparison theorems for a generalized modulus of continuity
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43943/1/11512_2006_Article_BF02383639.pd
Local Hardy Spaces of Musielak-Orlicz Type and Their Applications
Let \phi: \mathbb{R}^n\times[0,\fz)\rightarrow[0,\fz) be a function such
that is an Orlicz function and (the class of local weights
introduced by V. S. Rychkov). In this paper, the authors introduce a local
Hardy space of Musielak-Orlicz type by the local grand
maximal function, and a local -type space
which is further proved to be the
dual space of . As an application, the authors prove
that the class of pointwise multipliers for the local
-type space ,
characterized by E. Nakai and K. Yabuta, is just the dual of
L^1(\rn)+h_{\Phi_0}(\mathbb{R}^n), where is an increasing function on
satisfying some additional growth conditions and a
Musielak-Orlicz function induced by . Characterizations of
, including the atoms, the local vertical and the local
nontangential maximal functions, are presented. Using the atomic
characterization, the authors prove the existence of finite atomic
decompositions achieving the norm in some dense subspaces of
, from which, the authors further deduce some
criterions for the boundedness on of some sublinear
operators. Finally, the authors show that the local Riesz transforms and some
pseudo-differential operators are bounded on .Comment: Sci. China Math. (to appear
Fourier analysis on local fields (MN-15)
This book presents a development of the basic facts about harmonic analysis on local fields and the n-dimensional vector spaces over these fields. It focuses almost exclusively on the analogy between the local field and Euclidean cases, with respect to the form of statements, the manner of proof, and the variety of applications. The force of the analogy between the local field and Euclidean cases rests in the relationship of the field structures that underlie the respective cases. A complete classification of locally compact, non-discrete fields gives us two examples of connected fields (re
A maximal function characterization of weighted Besov-Lipschitz and Triebel-Lizorkin spaces.
We give characterizations of weighted Besov-Lipschitz and Triebel-Lizorkin spaces with weights via a smooth kernel which satisfies "minimal" moment and Tauberian conditions. The results are stated in terms of the mixed norm of a certain maximal function of a distribution in these weighted spaces
A maximal function characterization of weighted Besov-Lipschitz and Triebel-Lizorkin spaces
We give characterizations of weighted Besov-Lipschitz and Triebel-Lizorkin spaces with A∞ weights via a smooth kernel which satisfies "minimal" moment and
Tauberian conditions. The results are stated in terms of the mixed norm of certain
maximal function of a distribution in these weighted spaces
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