Normal operators

Goldstein, M.

doi:10.1090/s0002-9939-1969-0251214-8

Cited by 2 publications

(1 citation statement)

References 9 publications

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“…However, the details of the phenomenon are not consistent with other work on distortion products. First, although the slopes of the Weber fraction are compatible with a quadratic distortion, the low levels at which the departures from Weber's law are seen are inconsistent with previous tone-cancellation studies (Goldstein, 1967). Secondly, the departures from Weber's law are seen at 4 and 8 kHz, with signals whose bandwidths are less than that of the critical band, so that any cubic difference tone will not be resolved by the auditory system.…”

Section: And--ocontrolcontrasting

confidence: 62%

Proceedings of the Physiological Society, 24‐25 April 1987, Newcastle Meeting: Communications

Iravani¹,

Zar²

1987

The Journal of Physiology

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Section: And--ocontrolcontrasting

confidence: 62%

Proceedings of the Physiological Society, 24‐25 April 1987, Newcastle Meeting: Communications

Iravani¹,

Zar²

1987

The Journal of Physiology

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A new operator for elliptic equations, and theP-compactification for ?u=Pu

Nakai

Sario

1970

Math. Ann.

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MITSURU NAKAI and LEO SARIOAll operators considered thus far in the principal function problem have been associated with Dirichlet data on the relative boundary (see Bibliography). In view of the unconditional solvability of the Neumann problem for certain partial differential equations it is important to also consider the case of given Neumann data on the relative boundary. We shall take a somewhat more general viewpoint and introduce a new operator, which we call the principal operator, associated with a linear combination of Dirichlet and Neumann data and defined by properties (L.1)-(L.4) less stringent than those of any known operator.The principal function problem has thus far been solved only for the Laplace equation on Riemann surfaces and Riemannian manifolds. We shall show that the solution exists for arbitrary elliptic Eqs. (1) with (2) on arbitrary manifolds.As an application we consider P-harmonic functions, i.e., solutions of the equation Au = Pu, P >__ O, P ~g O. We establish the existence of the Robin operator defined by the behavior Ou/On+hu= 0 on the (ideal) harmonic boundary. The corresponding principal function is the Robin function on an arbitrary manifold. The existence of this function, of well-known importance in the theory of heat conduction (see e.g. Bergman-Schiffer [3]), has been known only for regions with smooth boundaries.The harmonic boundary referred to above is in what we call the P-eompactification of a manifold, specifically formed to study P-harmonic functions. It has significance in its own right in compactification and classification theory.

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Normal operators

Cited by 2 publications

References 9 publications

Proceedings of the Physiological Society, 24‐25 April 1987, Newcastle Meeting: Communications

Proceedings of the Physiological Society, 24‐25 April 1987, Newcastle Meeting: Communications

A new operator for elliptic equations, and theP-compactification for ?u=Pu

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