TY - JOUR

T1 - Fourier Integrals, Special Functions, and the Semicontinuity Phenomenon

AU - Palamodov, V. P.

PY - 2001

Y1 - 2001

N2 - For a real weighted homogeneous hypersurface germ, we consider elliptic deformations and related special functions. Singularities of these special functions are characterized by some rational numbers called energy exponents. We apply the residue mapping to the corresponding Fourier integrals and give a geometric interpretation of the energy exponents in the terms of the volume of the associated Lagrangian manifold. The energy exponents are calculated for a series of examples. Two conjectures concerning the energy exponents are discussed.

AB - For a real weighted homogeneous hypersurface germ, we consider elliptic deformations and related special functions. Singularities of these special functions are characterized by some rational numbers called energy exponents. We apply the residue mapping to the corresponding Fourier integrals and give a geometric interpretation of the energy exponents in the terms of the volume of the associated Lagrangian manifold. The energy exponents are calculated for a series of examples. Two conjectures concerning the energy exponents are discussed.

UR - http://www.scopus.com/inward/record.url?scp=0035640165&partnerID=8YFLogxK

U2 - 10.1023/A:1017579232328

DO - 10.1023/A:1017579232328

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AN - SCOPUS:0035640165

SN - 0016-2663

VL - 35

SP - 124

EP - 132

JO - Functional Analysis and its Applications

JF - Functional Analysis and its Applications

IS - 2

M1 - 343254

ER -