177,268 research outputs found
The Balian-Low theorem for symplectic lattices in higher dimensions
No full textThe Balian-Low theorem expresses the fact that time-frequency concentration is incompatible with non-redundancy for Gabor systems that form orthonormal or Riesz bases for L-2(R). We extend the Balian-Low theorem for Riesz bases to higher dimensions, obtaining a weak form valid for all sets of time-frequency shifts which form a lattice in R-2d, and a strong form valid for symplectic lattices in R-2d. For the orthonormal basis case, we obtain a strong form valid for general non-lattice sets which are symmetric with respect to the origin. (C) 2002 Elsevier Science (USA). All rights reserved
A Balian-Low theorem for subspaces
No full textWe extend the Balian–Low theorem to Gabor subspaces of L2(R) by involving the concept of additional time–frequency shift invariance. We prove that if a Gabor system on a lattice of rational density is a Riesz sequence generating a subspace which is invariant under an additional time–frequency shift, then its generator cannot decay fast simultaneously in time and frequency
The Balian–Low theorem for symplectic lattices in higher dimensions
No full textAbstractThe Balian–Low theorem expresses the fact that time–frequency concentration is incompatible with non-redundancy for Gabor systems that form orthonormal or Riesz bases for L2(R). We extend the Balian–Low theorem for Riesz bases to higher dimensions, obtaining a weak form valid for all sets of time–frequency shifts which form a lattice in R2d, and a strong form valid for symplectic lattices in R2d. For the orthonormal basis case, we obtain a strong form valid for general non-lattice sets which are symmetric with respect to the origin
Fungsi Tari Balian Bawo Dalam Upacara Nyirinyiau Pada Masyarakat Dayak Lawangan Di Kabupaten Barito Timur
No full textTari Balian Bawo merupakan tari penyembuhan atau pembersihan yang
dipercaya masyarakat Dayak Lawangan di Kabupaten Barito Timur melalui sebuah
upacara ritual. Tari Balian Bawo merupakan suatu tari yang disakralkan oleh
masyarakat setempat, yang menjadi bagian dari beberapa upacara adat yang hingga saat ini masih dipertahankan keberadaannya salah satunya untuk upacara Nyirinyiau. Balian Bawo berperan penting dalam siklus kehidupan sejak kelahiran sampai pada kematian Pokok permasalahan penelitian ini adalah fungsi tari Balian Bawo dalam upacara Nyirinyiau pada masyarakat Dayak Lawangan di Kabupaten Barito Timur. Untuk membantu menemukan jawaban dari permasalahan, dipakai teori Radcliffe Brown mengenai Struktur dan Fungsi. Menurut A. R Radcliffe Brown fungsi adalah bagian suatu kegiatan yang berguna di mana kegiatan tersebut bertindak sesuai bidang atau tujuan yang dilakukan secara menyeluruh. Dalam kehidupan sosial, Brown menspesifikasikan keadaan sistem ke dalam hubungannya dengan fungsifungsi proses sosial, sebagai kelangsungan sistem. Melalui fungsi struktur dapat berpengaruh dalam kehidupan secara keseluruha
New Proof for Balian-Low Theorem of Nonlinear Gabor System
No full textThe main purpose of this paper is to give a new proof of the Balian-Low theorem for Gabor system { (2 ) ( − ), , ∈ Z}, which is proposed by Fu et al. and associated with nonlinear Fourier atoms. To this end, we establish the relationships between spaces 2 (R, ) and 2 (R). We also introduce the concept of frame associated with nonlinear Fourier atoms for 2 (R, ) and obtain many subsidiary results for this kind of (Gabor) frames
Extra invariance and Balian-Low type obstructions for Gabor spaces
No full textWe establish some Balian-Low type results for Gabor spaces, which concern with discontinuity in some periodization of , where is the Zak transform of the window function .
The results are compared with the case for shift-invariant spaces where the Zak transform is replaced by Fourier transform
A quantitative subspace Balian-Low theorem
No full textLet G⊂L2(R) be the subspace spanned by a Gabor Riesz sequence (g,Λ) with g∈L2(R) and a lattice Λ⊂R2 of rational density. It was shown recently that if g is well-localized both in time and frequency, then G cannot contain any time-frequency shift π(z)g of g with z∉Λ. In this paper, we improve the result to the quantitative statement that the L2-distance of π(z)g to the space G is equivalent to the Euclidean distance of z to the lattice Λ, in the sense that the ratio between those two distances is uniformly bounded above and below by positive constants. On the way, we prove several results of independent interest, one of them being closely related to the so-called weak Balian-Low theorem for subspaces
Differentiation And The Balian-Low Theorem
No full text. The Balian--Low theorem (BLT) is a key result in time-frequency analysis, originally stated by Balian and, independently, by Low, as: If a Gabor system fe 2ßimbt g(t \Gamma na)g m;n2Z with ab = 1 forms an orthonormal basis for L 2 (R), then `Z 1 \Gamma1 jt g(t)j 2 dt ' `Z 1 \Gamma1 jfl g(fl)j 2 dfl ' = +1: The BLT was later extended from orthonormal bases to exact frames. This paper presents a tutorial on Gabor systems, the BLT, and related topics, such as the Zak transform and Wilson bases. Because of the fact that (g 0 ) (fl) = 2ßifl g(fl), the role of differentiation in the proof of the BLT is examined carefully. The major new contributions of this paper are the construction of a complete Gabor system of the form fe 2ßibm t g(t \Gamma an )g such that f(an ; bm )g has density strictly less than 1, an Amalgam BLT that provides distinct restrictions on Gabor systems fe 2ßimbt g(t \Gamma na)g that form exact frames, and a new proof of the BLT for exact frame..
The geometry generated by quantum entropy
No full textURL: http://www-spht.cea.fr/articles/T93/007 AbstractIn quantum statistical mechanics, the observables and the states are described by operators, which are regarded in the Liouville representation as vectors belonging to two dual spaces. Apart from their scalar products, which describe the expectation values of physical quantities in the considered state, the only scalar which has a physical meaning is the entropy of von Neumann It is thus natural to introduce in the space of states a metric structure generated by the infinitesimal distance If we regard the matrix elements of as covariant coordinates, the contravariant coordinates are In the classical limit, the curvature of this Liouville space, regarded as a Riemannian manifold, vanishes. For equilibrium thermodynamics, the metric which is induced on the macroscopic variables describes the correspondence between canonically conjugate pairs. The reduction of non-equilibrium statistical mechanics to non-equilibrium thermodynamics can be described by means of the Nakajima-Zwanzig projection method, which associates with any state a macroscopically equivalent simpler state having a canonical form; in terms of the natural metric, this reduction appears as an orthogonal projection. \underbar{Reference} : R. Balian, Y. Alhassid and H. Reinhardt, {\sl Phys. Reports\/} {\bf 131} (1986) 1-146. %{\it Abstract for STA Forum on ``Information and Geometry'' , Hakone, Japan, 14-20 March 1993
A quantitative subspace Balian-Low theorem
No full textLet G⊂L2(R) be the subspace spanned by a Gabor Riesz sequence (g,Λ) with g∈L2(R) and a lattice Λ⊂R2 of rational density. It was shown recently that if g is well-localized both in time and frequency, then G cannot contain any time-frequency shift π(z)g of g with z∉Λ. In this paper, we improve the result to the quantitative statement that the L2-distance of π(z)g to the space G is equivalent to the Euclidean distance of z to the lattice Λ, in the sense that the ratio between those two distances is uniformly bounded above and below by positive constants. On the way, we prove several results of independent interest, one of them being closely related to the so-called weak Balian-Low theorem for subspaces
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