LEADER 01444nam 2200397 a 450 001 9910692681403321 005 20040811135951.0 035 $a(CKB)5470000002354648 035 $a(OCoLC)56132275 035 9 $aocm56132275 035 $a(OCoLC)995470000002354648 035 $a(EXLCZ)995470000002354648 100 $a20040811d2004 ua 0 101 0 $aeng 135 $aurmn|||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aWildland fires$b[electronic resource] $eForest Service and BLM need better information and systematic approach for assessing the risks of environmental effects : report to congressional requesters 210 1$a[Washington, D.C.] :$cU.S. General Accounting Office,$d[2004] 300 $aTitle from title screen (viewed on Aug. 6, 2004). 300 $a"June 2004." 300 $aPaper version available from: U.S. General Accounting Office, 441 G St., NW, Rm. LM, Washington, D.C. 20548. 300 $a"GAO-04-705." 320 $aIncludes bibliographical references. 517 $aWildland fires 606 $aWildfires$xEnvironmental aspects 615 0$aWildfires$xEnvironmental aspects. 712 02$aUnited States.$bForest Service. 712 02$aUnited States.$bBureau of Land Management. 801 0$bGPO 801 1$bGPO 906 $aBOOK 912 $a9910692681403321 996 $aWildland fires$93423285 997 $aUNINA LEADER 04322nam 22006133 450 001 9910958126703321 005 20231110212634.0 010 $a9781470470258 010 $a147047025X 035 $a(MiAaPQ)EBC6939724 035 $a(Au-PeEL)EBL6939724 035 $a(CKB)21420567900041 035 $a(OCoLC)1312158592 035 $a(EXLCZ)9921420567900041 100 $a20220327d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aPositive Gaussian Kernels Also Have Gaussian Minimizers 205 $a1st ed. 210 1$aProvidence :$cAmerican Mathematical Society,$d2022. 210 4$dİ2022. 215 $a1 online resource (102 pages) 225 1 $aMemoirs of the American Mathematical Society ;$vv.276 311 08$aPrint version: Barthe, Franck Positive Gaussian Kernels Also Have Gaussian Minimizers Providence : American Mathematical Society,c2022 9781470451431 327 $aCover -- Title page -- Chapter 1. Introduction -- 1.1. Background and motivation -- 1.2. Notation and main results -- 1.3. Acknowledgments -- Chapter 2. Well-posedness of the Minimization Problem and the Minimum Value -- 2.1. A non-degeneracy condition -- 2.2. Calculations for centered Gaussian functions -- 2.3. Ensuring finiteness for some functions -- 2.4. On the effect of translating Gaussian functions and consequences of positivity -- 2.5. Case analysis and non-degeneracy hypotheses -- Chapter 3. Proof of the Main Theorem -- 3.1. Decomposition of the kernel -- 3.2. More on quadratic forms -- 3.3. Preliminaries and general strategy of the proof -- 3.4. Optimal transport map -- 3.5. Classes of test functions -- 3.6. Transportation argument -- 3.7. Surjectivity of the change of variable map -- 3.8. Approximation argument -- Chapter 4. Geometric Brascamp-Lieb Inequality -- 4.1. Finding the infimum on centered Gaussian functions -- 4.2. Geometric version of Inverse Brascamp-Lieb inequalities -- 4.3. Relation with the results of Chen, Dafnis and Paouris -- Chapter 5. Dual Form of Inverse Brascamp-Lieb Inequalities -- Chapter 6. Interpolation -- Chapter 7. Positivity in the Rank One Case -- 7.1. No kernel -- 7.2. With a kernel -- Chapter 8. Positivity Condition in the General Case -- 8.1. Recursive structure of the problem -- 8.2. Formulation of the characterization result -- 8.3. Useful notation for the proof -- 8.4. Necessity of Condition (C) -- 8.5. Sufficiency of Condition (C) -- Bibliography -- Back Cover. 330 $a"We study lower bounds on multilinear operators with Gaussian kernels acting on Lebesgue spaces, with exponents below one. We put forward natural conditions when the optimal constant can be computed by inspecting centered Gaussian functions only, and we give necessary and sufficient conditions for this constant to be positive. Our work provides a counterpart to Lieb's results on maximizers of multilinear operators with real Gaussian kernels, also known as the multidimensional Brascamp-Lieb inequality. It unifies and extends several inverse inequalities"--$cProvided by publisher. 410 0$aMemoirs of the American Mathematical Society 606 $aGaussian processes 606 $aKernel functions 606 $aInequalities (Mathematics) 606 $aIntegral operators 606 $aReal functions -- Inequalities -- Inequalities for sums, series and integrals$2msc 606 $aOperator theory -- Integral, integro-differential, and pseudodifferential operators -- Integral operators$2msc 615 0$aGaussian processes. 615 0$aKernel functions. 615 0$aInequalities (Mathematics) 615 0$aIntegral operators. 615 7$aReal functions -- Inequalities -- Inequalities for sums, series and integrals. 615 7$aOperator theory -- Integral, integro-differential, and pseudodifferential operators -- Integral operators. 676 $a519.2/3 676 $a519.23 686 $a26D15$a47G10$2msc 700 $aBarthe$b Franck$01799928 701 $aWolff$b Pawe?$01799929 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910958126703321 996 $aPositive Gaussian Kernels Also Have Gaussian Minimizers$94344357 997 $aUNINA