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Dirichlet boundary conditionDirichlet's unit theoremDirichlet distributionDirichlet processPoisson kernelDirichlet convolutionDirichlet-multinomial distributionDirichlet problemFredholm integral equationLipschitz continuityDirichlet l-functionFunctional analysisReproducing kernel hilbert spaceLaplace operatorDirichlet functionDirichlet energyParseval's identityKernel density estimationDarboux integralBeta functionLaplace distributionPositive-definite kernelMathematical analysisSchwartz kernel theoremLeibniz formula for determinantsFisher kernelKronecker deltaJensen's inequalitySpecial values of l-functionsGaussian functionGeneralized dirichlet distributionRiemann-stieltjes integralKoenigs functionLegendre transformationLagrange inversion theoremGraph fourier transformK-functionP-adic analysisLebesgue measureSpectrumDirichlet's testD'alembert's equationSchwarz lemmaTransition kernelKernel embedding of distributionsLaplace's equationBochner integralBloch's theoremDifferential operatorRiemann sphereWalsh functionLaplace's methodMathieu functionLeibniz integral ruleKilling formPythagorean theoremComplex analysisLerch zeta functionHellinger integralOperator theoryCharacteristic functionProbability density functionHessian matrixFourier analysisCauchy's integral formulaHypercomplex analysisDiscrete laplace operatorComplex measureDarboux's theoremSobolev spaceLiouville functionAsymmetric laplace distributionCarleson's theoremDirichlet's approximation theoremLagrangian functionSchur decompositionGaussian random fieldLaplacian matrixDirichlet conditionsMeasure theoryDeterminantal point processOrlicz spaceHeat kernelDirichlet seriesMarkov kernelResolvent formalismEuler's formulaDirac combKernelProbability-generating functionPoisson summation formulaFrobenius methodLebesgue covering dimensionOrdinary differential equationGlobal analysisHilbert transformConvex conjugatePseudodifferential operatorAnalytic continuationDiscrete-time fourier transform