Search results for "Bessel"

showing 3 items of 73 documents

Stealth dicing with Bessel beams and beyond

2016

In the context of laser cutting of transparent materials, we investigate glass cleaving with Bessel beams and report that a modification of the beam with 3 main lobes drastically enhances cleavability and reduces defects.

symbols.namesakeOpticsMaterials processingMaterials sciencebusiness.industryLaser cuttingsymbolsBeam shapingWafer dicingContext (language use)businessBessel functionBeam (structure)Lasers Congress 2016 (ASSL, LSC, LAC)
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Bounds for Bessel functions

1989

We establish lower and upper bounds for the Bessel functionJ v (x) and the modified Bessel functionI v(x) of the first kind. Our chief tool is the differential equation satisfied by these functions.

symbols.namesakeParticle in a spherically symmetric potentialCylindrical harmonicsBessel processGeneral MathematicsMathematical analysisBessel polynomialsStruve functionsymbolsBessel's inequalityBessel functionLommel functionMathematicsRendiconti del Circolo Matematico di Palermo
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Riesz-Fischer Maps, Semi-frames and Frames in Rigged Hilbert Spaces

2021

In this note we present a review, some considerations and new results about maps with values in a distribution space and domain in a σ-finite measure space X. Namely, this is a survey about Bessel maps, frames and bases (in particular Riesz and Gel’fand bases) in a distribution space. In this setting, the Riesz-Fischer maps and semi-frames are defined and new results about them are obtained. Some examples in tempered distributions space are examined.

symbols.namesakePure mathematicsDistribution (mathematics)Settore MAT/05 - Analisi MatematicasymbolsHilbert spaceRigged Hilbert spaceSpace (mathematics)Measure (mathematics)Frames Bases Distributions Rigged Hilbert spaceBessel functionDomain (mathematical analysis)Mathematics
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