Analytic Of Khavinson D . Seattle August , 2019 I - - - PDF document

Variations ( Eternal ) the Theme on Continuation Analytic Of Khavinson D . Seattle August , 2019

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I 2- - Few facts : . ) , G. Lames Classical M Heine Ferrers ( E - . . . , , r :={x : 72×56 ; o } Priephg al > an a , , > , . . A ) in Du o r - { - Sr f pot deg N of u= . , polynomial " harmonic is Then U a , of degree N E . ' 92 ) The For H . Shapiro . S ( entire Oke any . , f the * ) data solution L of entire is a , . ) ' Armitage ( D refinement 04 - . . , ConjeetuuLhK-HSs)T Ellipsoids are which for domains holds THM the the only . ' d 5) ( Render TRUE H . . provided P=LPcx)=o . . , P polynomial Pmt D= Po - t . . . - ' , homogeneous " IR Pm in 7,0 ( i. elliptic e. ) . ,

13 - - Discussing - { C x. y ) T n 2 - - - , :xIyZltePn¥D=§ - ? ?7 n , " " quintic . a C E. Lundberg I ) true Ad for cuties hoc Render H . odd ? ? ? deg T " 75 intuition " , -2N " { " DP Data sits 2 T pieces of so on , becomes overdetermined due C to . ' aimi:F¥:::%:;c÷nT = { x' " + y 'Ll } " ' 's T : TV P Eben felt ⇐ screen . 92 ) ( ! singularities 0 many - × ( ) data for the xx x - . . xx A - XI . . f y = L s - EL ( DK 10 ) nearest ' the × , x 2314 f- 0,0 ) ( are n nom x

13 - - FindingSingularitiesT E. Lundberg . 5. Shapiro ( S Eben DK P felt , H Bell . . , , , ' to 105 - , " ( A. Kolmogorov " Lightning Bolts Arnold V. , !3th m ) ' 50 Pro # Hilbert 's s , . I :# X X closed LB a . ' C ! ) The size LB E in of close how to the origin the ~ singularity appears . Dim 3D virtually nothing HIGHER - . , except for imprecise rather is known estimates for elliptic Render of Surfaces .

14 - - Applicationsto.i.ir/-hogonalpelynomialsy try OP :L pfita.io 1122 B r -8mm ① , " . 2eeurre.nu , ( Pn OP - n ) Of deg LET my , put it an Zpn= an ,nPn - An + - Neff " - - Nti - : { ⇒ r 2K ' su o - m - u tf Pol deg . of n pot of deg u K = Ent . - N The ( M Putin . Stagliano polo ' 07 us ar , . N ) K polo Styli ' D us lo and - . , Either condition ⇒ N =3 e = , are Chebyshev ellipse Lpn } . , SOME Existence with domain no of hemp ert ' L 78 recurrence - . . ,

-=y C- I Eigenfunctions OTHER BVP - . :÷÷ " II T of a ? where Q singularities are . Essentially nothing known is - . ellipsoid ALL eigenfunctions A = - , type ) exponential entire ( of are - unpublished ) Render to K C H SS H - . , proofs ) Iad ' ' well ( unpublished ) C with known - , ? Conjecture ? If ALL eigenfunctions entire ellipsoid d i. an e. = , , , singularities out the shape " sound .

I 6- - be found References in can D . Lundberg Linear Ke E Holomorphic , Potential Classical PDE and a Monographs Theory , . Surveys Math , 2018 AMS 232 . , , Ln HappyEuerything.my ! ! John Don I FT ! CHEERS -