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### Approximation of entire function solutions of the Helmholtz equation having slow growth

Kumar, Devendra
Journal of Applied Analysis, 2012, Vol.18(2), pp.179-196 [Peer Reviewed Journal]
Walter de Gruyter GmbH
Available
Title: Approximation of entire function solutions of the Helmholtz equation having slow growth
Author: Kumar, Devendra
Publisher: Walter de Gruyter GmbH
Subject: Generalized Order ; Entire Function ; Helmholtz Equation ; Chebyshev Approximation Error
Description: In this paper, we study the Chebyshev polynomial approximation of entire solutions of Helmholtz equations in in Banach spaces ( space, Hardy space and Bergman space). Some bounds on generalized order of entire solutions of Helmholtz equations of slow growth have been obtained in terms of the coefficients and approximation errors using function theoretic methods.
Is part of: Journal of Applied Analysis, 2012, Vol.18(2), pp.179-196
Identifier: 1425-6908 (ISSN); 1869-6082 (E-ISSN); 10.1515/jaa-2012-0012 (DOI)
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### Generalized growth and best approximation of entire functions in L p -norm in several complex variables

Kumar, Devendra
ANNALI DELL'UNIVERSITA' DI FERRARA, 2011, Vol.57(2), pp.353-372 [Peer Reviewed Journal]
Springer Science & Business Media B.V.
Available
Title: Generalized growth and best approximation of entire functions in L p -norm in several complex variables
Author: Kumar, Devendra
Subject: Generalized order and type ; Extremal polynomials ; Approximation and interpolation errors ; Pluricomplex Green function and slow growth
Description: The paper deals with the characterization of generalized order and generalized type of entire functions in several complex variables in terms of the coefficients of the development with respect to the sequence of extremal polynomials and the best L p -approximation and interpolation errors, 0
Is part of: ANNALI DELL'UNIVERSITA' DI FERRARA, 2011, Vol.57(2), pp.353-372
Identifier: 0430-3202 (ISSN); 1827-1510 (E-ISSN); 10.1007/s11565-011-0130-8 (DOI)
• Several versions

### Convergence and Characterization of Wavelets Associated with Dilation Matrix in Variable Spaces

Kumar, Devendra
Journal of Mathematics, 2013, Vol.2013, 7 pages [Peer Reviewed Journal]

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### Generalized growth and approximation of entire function solution of Helmholtz equation in Banach spaces

Kumar, Devendra
ANNALI DELL'UNIVERSITA' DI FERRARA, 2016, Vol.62(1), pp.83-97 [Peer Reviewed Journal]
Springer Science & Business Media B.V.
Available
Title: Generalized growth and approximation of entire function solution of Helmholtz equation in Banach spaces
Author: Kumar, Devendra
Subject: Generalized order and type ; Helmholtz equation ; Polynomial approximation ; Smirnov space
Description: In this paper, we study the generalized growth and polynomial approximation of entire function solution of Helmholtz equation in $$R^2$$ R 2 in Smirnov spaces [ $$\varepsilon _p (S)$$ ε p ( S ) and $$\varepsilon ^{^\prime }_p(S), 1\le p\le \infty$$ ε p ′ ( S ) , 1 ≤ p ≤ ∞ ] where S is finitely simply connected domain in the complex plane with the boundary that belongs to the Al’per class (Izv AN SSSR Ser Matem 19(3):423–444, 1955). Some bounds on generalized order and generalized type of entire solution of Helmholtz equation have been obtained in terms of the coefficients and approximation errors using function theoretic methods. Our results extend and improve the results of Kumar (J Appl Anal 18:179–196, 2012).
Is part of: ANNALI DELL'UNIVERSITA' DI FERRARA, 2016, Vol.62(1), pp.83-97
Identifier: 0430-3202 (ISSN); 1827-1510 (E-ISSN); 10.1007/s11565-015-0233-8 (DOI)
• Several versions

### On the Rational Approximation of Analytic Functions Having Generalized Types of Rate of Growth

Kumar, Devendra
International Journal of Mathematics and Mathematical Sciences, 2012, Vol.2012, 10 pages [Peer Reviewed Journal]

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### Growth and approximation of solutions to a class of certain linear partial differential equations in ℝ N

Kumar, Devendra
Mathematica Slovaca, 2014, Vol.64(1), pp.139-154 [Peer Reviewed Journal]
Springer Science & Business Media B.V.
Available
Title: Growth and approximation of solutions to a class of certain linear partial differential equations in ℝ N
Author: Kumar, Devendra
Subject: axisymmetric harmonic polynomials ; axi-convex region ; order and type ; Lagrange polynomial ; approximation and interpolation errors ; Bergman operator and hypersphere
Description: In this paper we consider the equation ∇ 2 φ + A ( r 2 ) X · ∇φ + C ( r 2 ) φ = 0 for X ∈ ℝ N whose coefficients are entire functions of the variable r = | X |. Corresponding to a specified axially symmetric solution φ and set C n of ( n + 1) circles, an axially symmetric solution Λ n * ( x , η ; C n ) and Λ n ( x , η ; C n ) are found that interpolates to φ ( x , η ) on the C n and converges uniformly to φ ( x , η ) on certain axially symmetric domains. The main results are the characterization of growth parameters order and type in terms of axially symmetric harmonic polynomial approximation errors and Lagrange polynomial interpolation errors using the method developed in [MARDEN, M.: Axisymmetric harmonic interpolation polynomials in ℝ N , Trans. Amer. Math. Soc. 196 (1974), 385–402] and [MARDEN, M.: Value distribution of harmonic polynomials in several real variables , Trans. Amer. math. Soc. 159 (1971), 137–154].
Is part of: Mathematica Slovaca, 2014, Vol.64(1), pp.139-154
Identifier: 0139-9918 (ISSN); 1337-2211 (E-ISSN); 10.2478/s12175-013-0192-4 (DOI)
• Several versions

### Spin-glass like dynamics of ferromagnetic clusters in La$$_{0.75}$$Ba$$_{0.25}$$CoO$$_3$$

Kumar, Devendra
arXiv.org, Jan 8, 2016 [Peer Reviewed Journal]

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### Faculty Use of Internet Services at a University of Agriculture and Technology

Kumar, Devendra
Library Philosophy and Practice, Feb 2010, pp.1-8 [Peer Reviewed Journal]
© ProQuest LLC All rights reserved, ProQuest Library Science, Library & Information Science Abstracts, Publicly Available Content Database, Research Library China, ProQuest Research Library, ProQuest Central, Research Library (Alumni edition), Library and Information Science Abstracts (LISA), Library & Information Science Collection, ProQuest Central (new), ProQuest Central K-12, ProQuest Central Korea, Research Library Prep, Social Science Premium Collection, ProQuest Central Essentials, ProQuest Central China, ProQuest One Academic
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Title: Faculty Use of Internet Services at a University of Agriculture and Technology
Author: Kumar, Devendra
Is part of: Library Philosophy and Practice, Feb 2010, pp.1-8
Identifier: 15220222 (E-ISSN)
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### IMAGES IN CLINICAL MEDICINE. Eggshell Calcifications of the Bladder

Nepal, Pankaj, Kumar, Devendra
The New England journal of medicine, 25 February 2016, Vol.374(8), pp.e9 [Peer Reviewed Journal]
MEDLINE/PubMed (U.S. National Library of Medicine)
Available
Title: IMAGES IN CLINICAL MEDICINE. Eggshell Calcifications of the Bladder
Author: Nepal, Pankaj; Kumar, Devendra
Subject: Calcinosis -- Diagnostic Imaging ; Dysuria -- Etiology ; Schistosomiasis Haematobia -- Diagnostic Imaging ; Urinary Bladder Diseases -- Diagnostic Imaging
Description: A 43-year-old man presented with dysuria and intermittent hematuria. Similar episodes had occurred several times in the preceding 6 months, with episodes of rectal bleeding. CT revealed hydroureteronephrosis of the right ureter and kidney, with mural calcifications. A 43-year-old man presented with a 1-month history of dysuria and intermittent hematuria. Similar episodes had occurred several times in the 6 months preceding presentation, along with episodes of rectal bleeding. The physical examination was unremarkable. Laboratory investigations revealed an elevated albumin:creatinine ratio (96 mg of albumin per millimole of creatinine), with dysmorphic red cells in the urine. Two urine cultures were sterile. A serum schistosoma antibody titer was 1:256. Renal ultrasonography revealed mild hydroureteronephrosis. Computed tomography of the abdomen and pelvis without the administration of contrast material revealed hydroureteronephrosis of the right ureter and kidney,...
Is part of: The New England journal of medicine, 25 February 2016, Vol.374(8), pp.e9
Identifier: 1533-4406 (E-ISSN); 26933870 Version (PMID); 10.1056/NEJMicm1504759 (DOI)
• Several versions

### Measures of Growth of Entire Solutions of Generalized Axially Symmetric Helmholtz Equation

Kumar, Devendra, Singh, Rajbir
Journal of Complex Analysis, 2013, Vol.2013, 6 pages [Peer Reviewed Journal]