The uncertainty principle on Riemannian symmetric spaces of the noncompact type

Sengupta, Jyoti

doi:10.1090/s0002-9939-01-06318-3

Cited by 15 publications

(8 citation statements)

References 6 publications

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“…It is based on a reduction to a Euclidean situation by means of the Radon transform. This is a powerful technique that is commonly used to attack problems related to the uncertainty principle on symmetric spaces as well as on Euclidean spaces; see for instance [22,23,21,20]. In our situation, the important feature is that for functions satisfying (1), the composition of the Radon transform and a Euclidean Fourier transform gives the Helgason-Fourier transform.…”

Section: Introductionmentioning

confidence: 99%

Uncertainty principles for the Schrödinger equation on Riemannian symmetric spaces of the noncompact type

Pasquale¹,

Sundari²

2012

Ann. inst. Fourier

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International audienceLet X be a Riemannian symmetric space of the noncompact type. We prove that the solution of the time-dependent Schrödinger equation on X with square integrable initial condition f is identically zero at all times t whenever f and the solution at a time t 0 >0 are simultaneously very rapidly decreasing. The stated condition of rapid decrease is of Beurling type. Conditions respectively of Gelfand-Shilov, Cowling-Price and Hardy type are deduced

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Section: Introductionmentioning

confidence: 99%

Uncertainty principles for the Schrödinger equation on Riemannian symmetric spaces of the noncompact type

Pasquale¹,

Sundari²

2012

Ann. inst. Fourier

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“…Ebata [17] had analyzed a semi simple Lie groups. J. Sengupta [18] had studied Riemannian symmetric spaces. In Electromagnetic Imaging problems, Ghodgaonkar [19] proposed that the group representation theory to solve problems of electromagnetic imaging.…”

Section: A Insulator Defect Detection Methods and Group Theorymentioning

confidence: 99%

“…The logarithm map log R0 and exponential map exp R0 at R 0 on SO n associated with the Riemannian metric can be expressed in terms of the usual matrix logarithm log and exponential exp, it satisfies equation (18) and equation( 19) [34].…”

Section: F ()]mentioning

confidence: 99%

The Method of Insulator Defect Recognition Based on Group Theory

Deng

2021

IEEE Access

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The auto insulator defect recognition method is more efficient and reliable than manual method, and it has lots of application. The paper presents an insulator recognition method, and meanwhile it attempts to explore the intrinsic characteristics among different images. Then, based on that many transformations of the image have the structure of matrix Lie group;the paper proposes a method that can recognize the defect of insulator using the Lie group method. The simulation results show the effective of the method.

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“…Part (a) of Hardy's theorem was proved in [20], [4], [6], while part (b) was proved in [16], [22]. Part (a) of Cowling-Price theorem was proved in [19] and in [17] and part (b) was proved in [18]. Part (a) of Morgan's theorem was proved in [19].…”

Section: Consequences Of Beurling's Theoremmentioning

confidence: 98%

“…This shows that Beurling's theorem is the Master theorem. Some of the latter theorems (which follow from Beurling's) were proved independently on symmetric spaces in recent years by many authors (see [20,4,6,16,17,19,22,18] etc. ).…”

Section: Introductionmentioning

confidence: 96%