NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2014, 5 (5), P. 619–625
ON THE NUMBER OF EIGENVALUES OF THE FAMILY OF OPERATOR MATRICES
M. I. Muminov – Universiti Teknologi Malaysia, Faculty of Science, Department of Mathematical Sciences, 81310 UTM Johor Bahru, Malaysia; mmuminov@mail.ru
T. H. Rasulov – Bukhara State University, Faculty of Physics and Mathematics, 11 M. Ikbol str., Bukhara, 200100, Uzbekistan; 2rth@mail.ru
We consider the family of operator matrices H(K), K∈T3:=(-π, π)3 acting in the direct sum of zero-, one- and two-particle subspaces of the bosonic Fock space. We find a finite set Λ ⊂ T3 to establish the existence of infinitely many eigenvalues of H(K) for all K ∈ Λ when the associated Friedrichs model has a zero energy resonance. It is found that for every K ∈ Λ the number N(K; z) of eigenvalues of H(K) lying on the left of z, z < 0, satisfies the asymptotic relation lim(z→-0)N(k, z)|log|z||-1 = u0 with 0 < u0 < ∞, independently on the cardinality of Λ. Moreover, we show that for any K ∈ Λ the operator H(K) has a finite number of negative eigenvalues if the associated Friedrichs model has a zero eigenvalue or a zero is the regular type point for positive definite Friedrichs model.
Keywords: operator matrix, bosonic Fock space, annihilation and creation operators, Friedrichs model, essential spectrum, asymptotics.
PACS 02.30.Tb
pin-up oyunu: pin up 306 – pinup az
http://pinupaz.bid/# pin up azerbaijan pin up azerbaijan
https://gabapentin.auction/# neurontin 300 mg buy
http://gabapentin.auction/# medicine neurontin 300 mg
https://gabapentin.auction/# neurontin
http://gabapentin.auction/# neurontin 300mg
http://semaglutide.win/# rybelsus cost
http://stromectol.agency/# ivermectin where to buy
https://gabapentin.auction/# neurontin capsule 400 mg
http://stromectol.agency/# minocycline pill
https://semaglutide.win/# Buy semaglutide pills
http://semaglutide.win/# buy semaglutide online
https://gabapentin.auction/# gabapentin 300mg
http://zithromax.company/# zithromax 500 mg lowest price pharmacy online
http://stromectol.agency/# price of ivermectin tablets
pump for ed: ed remedies – ed medicine
buying from online mexican pharmacy: buying prescription drugs in mexico online – mexico drug stores pharmacies
buy medicines online in india: indian pharmacy paypal – top 10 online pharmacy in india
mexican drugstore online: best online pharmacies in mexico – mexican rx online
Приватные круизы по островам https://arendakaterphuket.store/ Приобретаете ферза через гидрофитных видов спорта таковских как экстрим-спорт а также парасейлинг с катером унтер рукой.
https://rybelsus.icu/# rybelsus price ed drugs online from canada
https://clopidogrel.pro/# plavix medication comparison of ed drugs
https://paxlovid1st.shop/# buy paxlovid online errection problem cure
rybelsus.icu buy rybelsus or more https://toolbarqueries.google.ki/url?sa=t&url=https://rybelsus.icu cheaper more order Rybelsus and buy semaglutide online buy semaglutide online
https://paxlovid1st.shop/# paxlovid buy treatments for ed
https://clopidogrel.pro/# buy plavix ed help
rybelsus cost more or rybelsus cost http://dl.theme-wordpress.ir/index.php?url=http://rybelsus.icu good price rybelsus cost rybelsus and rybelsus cost Semaglutide pharmacy price
http://clopidogrel.pro/# buy Clopidogrel over the counter best medicine for ed
http://rybelsus.icu/# Buy semaglutide cheap ed pills
buy rybelsus rybelsus cost or more https://www.google.com.ph/url?sa=t&url=https://rybelsus.icu Buy semaglutide buy semaglutide online cheaper and order Rybelsus rybelsus price
pinup az: pin up 306 – pinup az
пин ап: пин ап – пин ап официальный сайт
slot casino siteleri: canl? casino siteleri – en iyi casino siteleri
casino siteleri: h?zl? casino – cazino
1xbet зеркало 1xbet зеркало or 1хставка http://maps.google.co.vi/url?q=https://1winrussia.online 1xbet 1хставка 1хбет and 1xbet официальный сайт 1xbet
cazino: dunyan?n en iyi casino siteleri – casino oyunlar?
canl? casino siteleri: casino oyunlar? – cazino
pin up 306: pin up – pin-up casino giris
viagra without a doctor prescription: vacuum therapy for ed – best canadian online pharmacy
best online pharmacy india: indian pharmacy – indian pharmacy
After all, what a great site and informative posts, I will upload inbound link – bookmark this web site? Regards, Reader.
medication from mexico pharmacy: reputable mexican pharmacies online – mexican drugstore online
online shopping pharmacy india indian pharmacies safe or world pharmacy india https://cse.google.td/url?sa=t&url=https://indianpharm1st.com reputable indian online pharmacy top online pharmacy india Online medicine home delivery and top 10 pharmacies in india best india pharmacy
cheap medications: pills erectile dysfunction – ed pills comparison
amoxicillin without a doctors prescription: ed medication – can ed be cured
mexican rx online: mexico drug stores pharmacies – medication from mexico pharmacy
indian pharmacy indianpharmacy com or top online pharmacy india https://images.google.com.pr/url?q=https://indianpharm1st.com Online medicine home delivery reputable indian pharmacies indian pharmacy online and п»їlegitimate online pharmacies india top 10 pharmacies in india
ed medications list: cure ed – anti fungal pills without prescription
best india pharmacy: cheapest online pharmacy india – online pharmacy india
indian pharmacy reputable indian pharmacies or mail order pharmacy india http://j.lix7.net/?http://indianpharm1st.com/ india pharmacy mail order buy medicines online in india п»їlegitimate online pharmacies india and online shopping pharmacy india best online pharmacy india
https://sweetbonanzatr.pro/# sweet bonanza tr
пин ап зеркало: пин ап казино – pinco
пин ап вход: Официальный Сайт – пинап казино
пин ап: Официальный Сайт – пин ап казино
пины: пины – пинап казино
пин ап казино: пинап – pin up kz
бонусы пин ап пин ап вход or pinco http://cse.google.co.ma/url?sa=t&url=http://pinupzerkalo.fun пин ап казино бонусы пин ап пин ап and пинко пинко
sweet bonanza: sweet bonanza – sweet bonanza oyna
Пин Ап Казино Официальный Сайт: пинап казино – pin up kz
пины Пин Ап Казахстан pin up kz
pin up: pin-up – pinup
пинко pinco or пинко https://cse.google.com.sb/url?q=https://pinupzerkalo.fun пинко пинап казино пинко and пин ап вход пин ап вход
пин ап зеркало: пин ап вход – пин ап вход
buy gabapentin: gabapentin best price – Neurontin online
Urgent Specialists: Rybelsus – semaglutide online
Regenerative Medicine Patient Portal or rybelsus price https://images.google.com.py/url?q=https://semaglutide.ink Specialists Patient Portal semaglutide and semaglutide rybelsus price
Urgent Specialists semaglutide or Specialists http://trackroad.com/conn/garminimport.aspx?returnurl=https://semaglutide.ink Rybelsus Rybelsus semaglutide online and Specialists Rybelsus
buy gabapentin: involves multisystem – buy gabapentin
involves multisystem: Neurontin online – gabapentin pro
buy medicines online in india indian pharm 24 buy prescription drugs from india
mexican drugstore online mexico pharmacy cheap п»їbest mexican online pharmacies
pharmacies in mexico that ship to usa mexican drugs reputable mexican pharmacies online
online pharmacy india best india pharmacy or top 10 pharmacies in india https://kultameren.fi/pennut/gotourl.php?url=http://indianpharm24.pro top 10 pharmacies in india reputable indian pharmacies best india pharmacy and п»їlegitimate online pharmacies india indian pharmacies safe
ed medications over the counter cheap drugs real viagra without a doctor prescription
best india pharmacy Indian pharmacy to USA buy prescription drugs from india
reputable indian online pharmacy India pharmacy delivery Online medicine home delivery
india pharmacy mail order top 10 pharmacies in india or indian pharmacy https://cse.google.fi/url?sa=t&source=web&url=https://indianpharm24.pro cheapest online pharmacy india indian pharmacy Online medicine home delivery and cheapest online pharmacy india top 10 online pharmacy in india
buy ed pills online cheap pharmacy top erection pills
mexican drugstore online mexico pharmacy mexican pharmaceuticals online
best india pharmacy reputable indian pharmacies or п»їlegitimate online pharmacies india https://www.google.nu/url?q=https://indianpharm24.pro india online pharmacy indianpharmacy com indian pharmacies safe and best online pharmacy india best india pharmacy
indian pharmacy paypal Best Indian pharmacy world pharmacy india
ed cure low cost pharmacy erectional dysfunction
deneme bonusu veren siteler denemebonusu2026.com http://slot-tr.online/# slot oyunlar?
deneme bonusu veren siteler deneme bonusu veren siteler yerliarama.org or deneme bonusu veren yeni siteler http://cttpeseux.ch/romands/link.php?url=http://denemebonusuverensiteler.top deneme bonusu veren siteler denemebonusu2026.com deneme bonusu veren siteler betturkey deneme bonusu veren siteler betturkey and deneme bonusu veren siteler yeni denemebonusuverensiteler.top
deneme bonusu veren yeni siteler http://casinositeleri.win/# Casino Siteleri
rybpharm canada rybpharm or buy rybelsus canada https://clapity.eu/redirect/?url=https://rybpharm.com buy rybelsus buy rybelsus online usa semaglutide and rybpharm canada buy rybelsus rybpharm
ED pills non prescription: ED meds online with insurance – cheapest ed pills ere pharm
rybpharm: rybpharm cheap semaglutide – buy rybelsus online usa
http://canadiandrugsgate.com/# ed medicine
best online pharmacies in mexico mexican border pharmacies shipping to usa or mexican mail order pharmacies https://alt1.toolbarqueries.google.co.ck/url?q=https://mexicanpharmgate.com mexico drug stores pharmacies mexican border pharmacies shipping to usa mexico drug stores pharmacies and buying prescription drugs in mexico buying prescription drugs in mexico
http://canadiandrugsgate.com/# diabetes and ed
Excellent blog here! Also your site loads up fast! What web host are you using? Can I get your affiliate link to your host? I wish my web site loaded up as fast as yours lol
amoxicillin tablet 500mg http://amoxilcompharm.com/# where to buy amoxicillin pharmacy
I really appreciate this post. I have been looking everywhere for this! Thank goodness I found it on Bing. You’ve made my day! Thanks again
This design is wicked! You most certainly know how to keep a reader amused. Between your wit and your videos, I was almost moved to start my own blog (well, almost…HaHa!) Great job. I really loved what you had to say, and more than that, how you presented it. Too cool!
purchase amoxicillin 500 mg http://clomidrexpharm.com/# where to buy generic clomid pills
Great work! This is the type of info that should be shared around the net. Shame on the search engines for not positioning this post higher! Come on over and visit my web site . Thanks =)
amoxicillin tablets in india http://amoxilcompharm.com/# can i purchase amoxicillin online
prednisone buy cheap prednisone 20 mg or prednisone prescription online https://maps.google.iq/url?q=https://prednisoneraypharm.com prednisone 25mg from canada how much is prednisone 5mg fast shipping prednisone and prednisone 25mg from canada 40 mg prednisone pill
I’ve read several good stuff here. Certainly worth bookmarking for revisiting. I surprise how much effort you put to make such a fantastic informative site.
Hi there very nice website!! Man .. Excellent .. Superb .. I’ll bookmark your website and take the feeds additionally…I’m satisfied to find so many helpful information right here within the submit, we’d like develop extra techniques in this regard, thank you for sharing.
I’m curious to find out what blog system you’re utilizing? I’m experiencing some small security problems with my latest website and I’d like to find something more safe. Do you have any suggestions?
prednisone 10 mg tablet prednisone without prescription medication or prednisone cream brand name http://whatsmywebsiteworth.info/value.php?site=prednisoneraypharm.com 50 mg prednisone canada pharmacy buying prednisone mexico fast shipping prednisone and prednisone prescription drug medicine prednisone 10mg
I think this is among the most important information for me. And i’m glad reading your article. But wanna remark on some general things, The web site style is wonderful, the articles is really nice : D. Good job, cheers
you have a great blog here! would you like to make some invite posts on my blog?
I’m still learning from you, but I’m trying to achieve my goals. I definitely enjoy reading everything that is written on your website.Keep the tips coming. I loved it!
You are a very intelligent individual!