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21.
The simple relation between representations of the covering groups of SL2 and GL2 makes it possible to fuse and extend the recent metaplectic results of Shimura, Waldspurger, Flicker, and ourselves. By giving a new (purely local andL-function theoretic) treatment of the Waldspurger-Shintani correspondence, we also simplify some of Waldspurger’s original results. 相似文献
22.
V. L. Topunov 《Acta Appl Math》1989,16(2):191-206
In this paper, an application of the Riquer-Thomas-Janet theory is described for the problem of transforming a system of partial differential equations into a passive form, i.e., to a special form which contains explicitly both the equations of the initial system and all their nontrivial differential consequences. This special representation of a system markedly facilitates the subsequent integration of the corresponding differential equations. In this paper, the modern approach to the indicated problem is presented. This is the approach adopted in the Knuth-Bendix procedure [13] for critical-pair/completion and then Buchberger's algorithm for completion of polynomial ideal bases [13] (or, alternatively, for the construction of Groebner bases for ideals in a differential operator ring [14]). The algorithm of reduction to the passive form for linear system of partial differential equations and its implementation in the algorithmic language REFAL, as well as the capabilities of the corresponding program, are outlined. Examples illustrating the power and efficiency of the system are presented. 相似文献
23.
G. L. Booth 《Acta Mathematica Hungarica》1989,54(3-4):201-208
24.
25.
L. A. Khalfin 《Journal of Mathematical Sciences》1987,36(5):616-626
The article surveys the main results of the statistical approach to the solution of ill-posed problems of mathematical physics, in application to specific ill-posed inverse problems in geophysics.Invited paper presented at the International Seminar on Mathematical Foundations of the Interpretation of Geophysical Fields, Moscow, May–June 1972.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 79, pp. 67–81, 1978. 相似文献
26.
27.
A. I. Shtern 《Russian Journal of Mathematical Physics》2006,13(2):210-223
As was proved by van der Waerden in 1933, every finite-dimensional locally bounded representation of a semisimple compact
Lie group is continuous. This is the famous “van der Waerden continuity theorem,” and it motivated a vast literature. In particular,
relationships between the assertion of the theorem (and of the inverse, in a sense, to this theorem) and some properties of
the Bohr compactifications of topological groups were established, which led to the introduction and the study of certain
classes of the so-called van der Waerden groups and algebras. Until now, after more than 70 years have passed, the van der
Waerden theorem appears in monographs and surveys in diverse forms; new proofs were found and then simplified in important
special cases.
In this paper, we prove that the statement of the van der Waerden theorem remains valid for all (not necessarily compact)
real semisimple Lie groups, i.e., any given finite-dimensional representation of a real semisimple Lie group is continuous
if and only if this representation is locally bounded.
More subtle results are also obtained. The main theorem contains several conditions equivalent to the continuity condition
for a finite-dimensional representation. In particular, it is proved that every finite-dimensional representation of a real
semisimple Lie group is continuous if and only if the restriction of this representation to the “compact” part, to the Abelian
part, or to the nilpotent part of the Iwasawa decomposition is locally bounded, and the original van der Waerden theorem is
also somewhat refined. For instance, the following assertion holds: every finite-dimensional representation of a compact semisimple
Lie group is continuous if and only if the restriction of this representation to some maximal torus is locally bounded.
Dedicated to the memory of George Mackey (1916–2006)
Partially supported by the Russian Foundation for Basic Research under grant no. 02-01-00574, by the Program of Supporting
the Leading Scientific Schools under grant no. NSh 619.203.1, and by the INTAS grant. 相似文献
28.
A. I. Nazarov 《Journal of Mathematical Sciences》2006,133(3):1314-1327
We find logarithmic small ball asymptotics for the L2-norm with respect to self-similar measures for a certain class of Gaussian processes including Brownian motion, Ornstein-Uhlenbeck
process, and their integrated counterparts. Bibliography: 46 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 311, 2004, pp. 190–213. 相似文献
29.
Using the method of the tensor Green’s function of the wave equation, the differential and total cross sections for the scattering of surface optical electromagnetic waves (surface plasmon polaritons) by a spherical nanoparticle into surface plasmon polaritons and light have been obtained with the inclusion of the magnetic dipole contribution. Using the example of noble metal systems, it has been shown that the magnetic dipole contribution may significantly affect the angular dependence of the differential cross sections and increase their anisotropy as the plasmon wavelength increases. 相似文献
30.
J. Maul I. Strachnov S. Karpuk P. Bernhard A. Oelsner G. Schönhense G. Huber 《Applied Physics A: Materials Science & Processing》2006,82(1):43-47
We report morphologic changes of metallic surfaces at the onset of ablation, starting from gentle ablation to the emergence of ablation craters. The evolution of both observed melting zones and of ablation craters therein are investigated in dependence of the ablation laser fluence for nanosecond ultraviolet laser pulses. Further, consequences of crater formation for cluster synthesis within the released atomic vapor are pointed out. PACS 52.38.Mf; 79.20.Ds; 65.40.De 相似文献