Methods Of Modern Mathematical Physics

By Kristian Kirsch. 2016

2,595 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ffbbe57867b5743de995ece01779cec458d1dfa0

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Citations in the corpus

3D bearing capacity probabilistic analyses of footings on spatially variable c–φ soil (2019, background): “The function (1) is positively defined (a sufficient and necessary condition according to Bochner’s theorem [34]), reflects separability of the fields under consideration, gives the possibility of distinct scales of fluctuation in three directions and is suggested by many researchers (e.”
Sharp polynomial decay rates for the damped wave equation on the torus (2012, methodology): “Using Proposition 10.1, together with the definition of the trace (see, for instance, [Reed and Simon 1980, Theorem VI.18]) we have 0= tr{m〈b〉3M3} = ∑ j∈N (m〈b〉3M3ẽ j 3, ẽ j 3)L2(T3) = ∑ j∈N γ j 3(〈b〉3ẽ j 3, ẽ j 3)L2(T3).”
Algebraic QFT in Curved Spacetime and Quasifree Hadamard States: An Introduction (2014, background): “Identity (75) is, in fact, correct and holds true also for m = 0 [55].”
Functional Analysis (2023, neutral): “(2) The eigenfunctions un are complete, that is, any nice function u(x) can be expanded into a generalized Fourier series”
Towards a Learning Theory of Cause-Effect Inference (2015, background): “The separability ofHk implies µk is Borel measurable iff it is weakly measurable (Reed & Simon, 1972, Thm. IV.22).”
On the phase transition in random simplicial complexes (2014, background): “Since G may be infinite and have unbounded degrees, we must resort to the theory of unbounded operators [28].”
On hyperboundedness and spectrum of Markov operators (2014, background): “Proof By the requirements imposed on the projection-valued family (Eλ)λ∈[−1,1] in the spectral Theorem (see for instance the chapter 7 of the book of Reed and Simon [2]), for any f ∈ L2(μ), the mapping [−1, 1] λ → μ[ f Eλ[ f ]] is non-decreasing.”
Equatorial Wave–Current Interactions (2019, background): “maps S(R) into S(R) and extends to a self-adjoint operator in L2(R) if and only if m is real-valued; see [40].”
Tensor product methods and entanglement optimization for ab initio quantum chemistry (2014, background): “In general, the symmetry operators of the Hamiltonian are the representations U of the symmetry group G on the Hilbert space, acting as U(g) H U−1(g) = H, (197) where U(g) is the unitary representation for the symmetry g ∈ G.”
Limit theorems for some branching measure-valued processes (2011, background): “If E is not bounded then we can see [21, 41].”
Schatten classes on compact manifolds: Kernel conditions☆ (2014, background): “For the basic theory of Schatten classes we refer the reader to [14,22,32,27].”