×

zbMATH — the first resource for mathematics

Classical boundary conditions as a technical tool in modern mathematical physics. (English) Zbl 0414.35069

MSC:
35Q99 Partial differential equations of mathematical physics and other areas of application
78A30 Electro- and magnetostatics
76W05 Magnetohydrodynamics and electrohydrodynamics
76E25 Stability and instability of magnetohydrodynamic and electrohydrodynamic flows
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Birman, M.S; Borzov, V.V, On the asymptotics of the discrete spectrum of some singular differential operators, Topics in math. phys., 5, 19-30, (1972)
[2] \scM. S. Birman and M. E. Solomjak, Lectures of the 1974 Ukranian Math Summer School, Kiev.
[3] \scZ. Ciesielski, “Lectúres on Brownian Motion, Heat Conduction and Potential Theory,” Arhus Lecture Notes. · Zbl 0232.60060
[4] \scA. Cooper and L. Rosen, The weakly coupled Yukawa^2 field theory: Cluster expansion and Wightman axioms, Trans. Amer. Math. Soc., in press.
[5] Courant, R; Hilbert, D, ()
[6] Cwickel, M, Weak type estimates for singular values and the number of bound states of Schrödinger operators, Ann. math., 106, 93-102, (1977)
[7] De Facio, B; Hammer, C.L, Remarks on the klauder phenomenon, J. math. phys., 15, 1071-1077, (1974)
[8] \scP. Deift, 1976 Princeton University Thesis; modified version, Princeton Series in Physics, Princeton Univ. Press, Princeton, N.J., in press,
[9] Deift, P; Simon, B, On the decoupling of finite singularities from the question of asymptotic completeness, J. functional analysis, 23, 218-238, (1976) · Zbl 0344.47007
[10] Faris, W, Self-adjoint operators, () · Zbl 0317.47016
[11] Fermi, E, Un metodo statistico per la determinazione di alcune priorietà dell’atome, Rend. acad. naz. lincei, 6, 602-607, (1927)
[12] Glimm, J; Jaffe, A; Spencer, T, The particle structure of the weakly coupled P(ø)2 model and other applications of high temperature expansions, II: the cluster expansion, ()
[13] Gombas, P, Die statistische theorie des atoms und ihre anwendunger, (1949), Springer-Verlag New York/Berlin · Zbl 0031.37703
[14] Hida, T, Stationary stochastic processes, (1970), Princeton Univ. Press Princeton, N.J · Zbl 0214.16401
[15] Ito, K; McKean, H, Diffusion processes and their sample paths, (1965), Springer-Verlag New York/Berlin · Zbl 0127.09503
[16] Kac, M, Can you hear the shape of a drum?, Amer. math. monthly, 73, No. 4, 1-23, (1966) · Zbl 0139.05603
[17] Kato, T, Perturbation theory for linear operators, (1966), Springer-Verlag New York/Berlin · Zbl 0148.12601
[18] Klauder, J, Field structure through model studies: aspects of nonrenormalizable theories, Acta phys. austriaca. suppl., XI, 341-387, (1973)
[19] Lieb, E, Bounds on the eigenvalues of the Laplace and Schrödinger operators, Bull. am. math. soc., 82, 751, (1976) · Zbl 0329.35018
[20] Lieb, E; Simon, B, The Thomas-Fermi theory of atoms, molecules and solids, Advances in math., 23, 22-116, (1977) · Zbl 0938.81568
[21] Lions, J.L, Lectures on elliptic partial differential equations, (1967), Tata Institute Bombay · Zbl 0253.35001
[22] March, N.H, The Thomas-Fermi approximation in quantum mechanics, Advances in phys., 6, 1-98, (1957) · Zbl 0077.23101
[23] Martin, A, Bound states in the strong coupling limit, Helv. phys. acta, 45, 140-148, (1972)
[24] Osterwalder, K; Schrader, R; Osterwalder, K; Schrader, R, Axioms for euclidean Green’s functions, I, II, Comm. math. phys., Comm. math. phys., 42, 281-305, (1975) · Zbl 0303.46034
[25] Reed, M; Simon, B, Methods of modern mathematical physics, I: functional analysis, (1972), Academic Press New York
[26] Reed, M; Simon, B, Methods of modern mathematical physics, II: Fourier analysis, self-adjointness, (1975), Academic Press New York · Zbl 0308.47002
[27] Reed, M; Simon, B, Methods of modern mathematical physics, IV: analysis of operators, (1978), Academic Press New York · Zbl 0401.47001
[28] Rosenbljum, G.V, The distribution of the discrete spectrum for singular differential operators, Dokl. akad. nauk SSSR, 202, 1012-1015, (1972)
[29] Simon, B, Quadratic forms and Klauder’s phenomenon: A remark on very singular perturbations, J. functional analysis, 14, 295-298, (1973) · Zbl 0268.47021
[30] Simon, B, The P(ø)2 Euclidean (quantum) field theory, (1974), Princeton Univ. Press Princeton, N.J
[31] Simon, B, Weak trace ideals and the number of bound states of Schrödinger operators, Trans. amer. math. soc., 224, 361-380, (1976) · Zbl 0348.47017
[32] Tamura, H, The asymptotic eigenvalue distribution for non-smooth elliptic operators, (), 19-22 · Zbl 0312.35058
[33] Thomas, L.H, The calculation of atomic fields, (), 542-548 · JFM 53.0868.04
[34] ()
[35] Weyl, H, Das asymptotische vertrielungsgesetz der eigenwerts linearer partieller differentialgleichungen, Math. ann., 71, 441-469, (1971)
[36] Lieb, E.H, Quantum mechanical extension of the Lebowitz-Penrose theorem on the van der Waals theory, J. math. phys., 7, 1016-1024, (1966)
[37] Robinson, D.W, The thermodynamic pressure in quantum statistical mechanics, (1971), Springer-Verlag Berlin
[38] Titchmarsh, E.C, Eigenfunction expansion, part 2, (1958), Canbridge Univ. Press London/New York · Zbl 0097.27601
[39] Davies, E.B, Helv. phys. acta, 48, 365-382, (1975)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.