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1.
Stephan Dahlke Gabriele Steidl Gerd Teschke 《Journal of Fourier Analysis and Applications》2004,10(5):507-539
This article is concerned with frame constructions on domains and manifolds. The
starting point is a unitary group representation which is square integrable modulo a suitable
subgroup and therefore gives rise to a generalized continuous wavelet transform. Then generalized
coorbit spaces can be defined by collecting all functions for which this wavelet transform
is contained in a weighted Lp-space. Moreover, we show that a judicious discretization of the
representation leads to an atomic decomposition and to Banach frames for these coorbit spaces. 相似文献
2.
3.
Synthesis of methyl 2-(3′-methoxy-4′-methylphenyl)-propionate via the T1(NO3)3-induced oxidative rearrangement of 3′-methoxy-4′-methylpropiophenone. 相似文献
4.
Stephan Dahlke Gitta Kutyniok Gabriele Steidl Gerd Teschke 《Applied and Computational Harmonic Analysis》2009,27(2):195-214
In this paper, we study the relationships of the newly developed continuous shearlet transform with the coorbit space theory. It turns out that all the conditions that are needed to apply the coorbit space theory can indeed be satisfied for the shearlet group. Consequently, we establish new families of smoothness spaces, the shearlet coorbit spaces. Moreover, our approach yields Banach frames for these spaces in a quite natural way. We also study the approximation power of best n-term approximation schemes and present some first numerical experiments. 相似文献
5.
In this paper, we are concerned with biorthogonal Wilson bases having B-splines as well as powers of sinc functions as window
functions. We prove properties of B-splines and exponential Euler splines and use these properties to estimate the Riesz bounds
of the Wilson bases. 相似文献
6.
Stephan Dahlke Gabriele Steidl Gerd Teschke 《Journal of Fourier Analysis and Applications》2007,13(4):387-403
The topic of this article is a generalization of the theory of coorbit spaces and related frame constructions to Banach spaces
of functions or distributions over domains and manifolds. As a special case one obtains modulation spaces and Gabor frames
on spheres. Group theoretical considerations allow first to introduce generalized wavelet transforms. These are then used
to define coorbit spaces on homogeneous spaces, which consist of functions having their generalized wavelet transform in some
weighted Lp space. We also describe natural ways of discretizing those wavelet transforms, or equivalently to obtain atomic decompositions
and Banach frames for the corresponding coorbit spaces. Based on these facts we treat aspects of nonlinear approximation and
show how the new theory can be applied to the Gabor transform on spheres. For the S1 we exhibit concrete examples of admissible Gabor atoms which are very closely related to uncertainty minimizing states. 相似文献
7.
Standard JM Steidl RJ Beecher MC Quandt RW 《The journal of physical chemistry. A》2011,115(7):1243-1249
Multireference configuration interaction (MRCI) calculations of the lowest singlet X(1A') and triplet ?((3)A') states as well as the first excited singlet ?((1)A') state have been performed for a series of bromocarbenes: CHBr, CFBr, CClBr, CBr(2), and CIBr. The MRCI calculations were performed with correlation consistent basis sets of valence triple-ζ plus polarization quality, employing a full-valence active space of 18 electrons in 12 orbitals (12 and 9, respectively, for CHBr). Results obtained include equilibrium geometries and harmonic vibrational frequencies for each of the electronic states, along with ?((3)A') ← X((1)A') singlet-triplet gaps and ?((1)A') ← X((1)A') transition energies. Comparisons have been made with previous computational and experimental results where available. The MRCI calculations presented in this work provide a comprehensive series of results at a consistent high level of theory for all of the bromocarbenes. 相似文献
8.
Consider the Vandermonde-like matrix , where the polynomials satisfy a three-term recurrence relation. If are the Chebyshev polynomials , then coincides with . This paper presents a new fast algorithm for the computation of the matrix-vector product in arithmetical operations. The algorithm divides into a fast transform which replaces with and a subsequent fast cosine transform. The first and central part of the algorithm is realized by a straightforward cascade summation based on properties of associated polynomials and by fast polynomial multiplications. Numerical tests demonstrate that our fast polynomial transform realizes with almost the same precision as the Clenshaw algorithm, but is much faster for .
9.
Standard JM Copack BA Johnson TK Przybyla DE Graham SR Steidl RJ 《The journal of physical chemistry. A》2008,112(2):336-341
Sulfur ylides are useful synthetic intermediates that are formed from the interaction between singlet carbenes and sulfur-containing molecules. Partial double-bond character frequently has been proposed as a key contributor to the stability of sulfur ylides. Calculations at the B3LYP, MP2, and CCSD(T) levels of theory employing various basis sets have been performed on the sulfur ylides H(2)S-CH(2) and (CH(3))(2)S-CH(2) in order to investigate the structure and bonding of these systems. The following general properties of sulfur ylides were observed from the computational studies: C-S bond distances that are close in length to that of a typical C-S double bond, high charge transfer from the sulfide to the carbene, and large torsional rotation barriers. Analysis of the sulfur ylide charge distribution indicates that the unusually short C-S bond distance can be attributed in part to the electrostatic attraction between highly oppositely charged carbon and sulfur atoms. Furthermore, n --> sigma* stabilization arising from donation of electron density from the carbon lone pair orbital into S-H or S-C antibonding orbitals leads to larger than expected torsional barriers. Finally, natural resonance theory analysis indicates that the bond order of the sulfur ylides H(2)S-CH(2) and (CH(3))(2)S-CH(2) is 1.4-1.5, intermediate between a single and double bond. 相似文献
10.
Stephan?Dahlke Filippo?De Mari Ernesto?De Vito S?ren?H?userEmail author Gabriele?Steidl Gerd?Teschke 《Journal of Geometric Analysis》2016,26(3):1693-1729
Recently, shearlet groups have received much attention in connection with shearlet transforms applied for orientation sensitive image analysis and restoration. The square integrable representations of the shearlet groups provide not only the basis for the shearlet transforms but also for a very natural definition of scales of smoothness spaces, called shearlet coorbit spaces. The aim of this paper is twofold: first we discover isomorphisms between shearlet groups and other well-known groups, namely extended Heisenberg groups and subgroups of the symplectic group. Interestingly, the connected shearlet group with positive dilations has an isomorphic copy in the symplectic group, while this is not true for the full shearlet group with all nonzero dilations. Indeed we prove the general result that there exist, up to adjoint action of the symplectic group, only one embedding of the extended Heisenberg algebra into the Lie algebra of the symplectic group. Having understood the various group isomorphisms it is natural to ask for the relations between coorbit spaces of isomorphic groups with equivalent representations. These connections are examined in the second part of the paper. We describe how isomorphic groups with equivalent representations lead to isomorphic coorbit spaces. In particular we apply this result to square integrable representations of the connected shearlet groups and metaplectic representations of subgroups of the symplectic group. This implies the definition of metaplectic coorbit spaces. Besides the usual full and connected shearlet groups we also deal with Toeplitz shearlet groups. 相似文献