Heat kernel
In the mathematical study of heat conduction and diffusion, a heat kernel is the fundamental solution to the heat equation on a specified domain with appropriate boundary conditions. It is also one of the main tools in the study of the spectrum of the Laplace operator, and is thus of some auxiliary importance throughout mathematical physics. The heat kernel represents the evolution of temperature in a region whose boundary is held fixed at a particular temperature (typically zero), such that an initial unit of heat energy is placed at a point at time t = 0. This solves the heat equation
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Alan Gaius Ramsay McIntoshCarl S. HerzCoherent states in mathematical physicsCurve-shortening flowDiffusion waveletsDirac delta functionDirac operatorFick's laws of diffusionGaussian functionGeometric Brownian motionGerhard HuiskenHeat equationHeat kernel equationHeat kernel signatureHuisken's monotonicity formulaIndex of physics articles (H)James R. NorrisKernelKernel density estimationManifoldManifold alignmentMaps of manifoldsMaria GordinaMean curvature flowMean squared displacementMehler kernelMinakshisundaram–Pleijel zeta functionMultiplier (Fourier analysis)Oscillator representationPoisson summation formulaPólya–Szegő inequalityQuantum fluctuationSegal–Bargmann spaceSpectral shape analysisSpectral tripleSubbaramiah MinakshisundaramThermal conductionTwo-dimensional Yang–Mills theoryZeta function (operator)Zeta function regularization
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Heat kernel
In the mathematical study of heat conduction and diffusion, a heat kernel is the fundamental solution to the heat equation on a specified domain with appropriate boundary conditions. It is also one of the main tools in the study of the spectrum of the Laplace operator, and is thus of some auxiliary importance throughout mathematical physics. The heat kernel represents the evolution of temperature in a region whose boundary is held fixed at a particular temperature (typically zero), such that an initial unit of heat energy is placed at a point at time t = 0. This solves the heat equation
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En el estudio matemático de la ...... ca en un punto en el momento .
@es
En mathématiques, le noyau de ...... en un point au temps initial.
@fr
In the mathematical study of h ...... lower bounds of Gaussian type.
@en
数学の特に熱伝導や拡散の研究に現れる熱核（ねつかく、英: h ...... 写像定理によって、次のような T の表現を得ることが出来る。
@ja
热核（英語：heat kernel）在数学中是指热方程的基本 ...... 意黎曼流形，当边界条件充分正则时，热核存在且在t>0时光滑。
@zh
해석학에서, 열핵(熱核, 영어: heat kernel)은 열 방정식의 그린 함수이다. 해석학에서 함수를 매끄럽게 만들기 위해 쓰인다.
@ko
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En el estudio matemático de la ...... ca en un punto en el momento .
@es
En mathématiques, le noyau de ...... en un point au temps initial.
@fr
In the mathematical study of h ...... This solves the heat equation
@en
数学の特に熱伝導や拡散の研究に現れる熱核（ねつかく、英: h ...... すものとなる。このとき、熱核は次のように表現される： (1)
@ja
热核（英語：heat kernel）在数学中是指热方程的基本 ...... 意黎曼流形，当边界条件充分正则时，热核存在且在t>0时光滑。
@zh
해석학에서, 열핵(熱核, 영어: heat kernel)은 열 방정식의 그린 함수이다. 해석학에서 함수를 매끄럽게 만들기 위해 쓰인다.
@ko
label
Heat kernel
@en
Kernel de calor
@es
Noyau de la chaleur
@fr
热核
@zh
熱核
@ja
열핵
@ko